mm-4879 === Subject: Re: Twin Paradox - Four Easy Solutions Ignorant Sean McHugh whined Androcles screamed (83): Strich9 has no idea what you're talking about. It's just important > that he declare that you have made a fatal error. That means you > should lie down because you're dead. > Apparently so. With the detractors (some at least), determination to > misunderstand SR is coupled with determination to misunderstand > English. It's a formidable combination. > Let's see you can misunderstand an inequality as well as plain English, > you miserable babbling wit. Over reaction would be an understatement. Perhaps Androcles needs > stronger medication. As for his using the 'Followup To' to try to > have this response diverted to a mock newsgroup, I don't think that > there is anything that he can take for being juvenile and corrupt. Personal attacks can be ignored. Do you have any physics to discuss, wit? > Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif > What kind of lunacy prompted Einstein to say > the speed of light from A to B is c-v, None, because he didn't say that. > the speed of light from B to A is c+v, He didn't say that either. > the time each way is the same? > So he didn't write http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif > In the frame where A and B are fixed on its x' axis, yes. In the frame > where A and B are moving with respect to its x axis, no. Bwhahahahaha! What the is an x' axis, cretin? > I'll get back to this later. Sure you will.... > For now let's look at Androcles' charge that > Einstein says that the speed of light is c+v and c-v. The gif'd formula that Androcles presented appears in Einstein's > original paper on Special Relativity. Applause, applause, Sean Mcwit has discovered where the terms c+v and c-v are found after it was pointed out to him! > Not only did he NOT say, [T]he > speed of light from A to B is c-v Where Einstein did not write: But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v , so it must have been Sean McIdiot. Simple denial shows Sean Mcwit for the incompetent illiterate cretin he is. === Subject: Re: Arithmetic Mean On May 22, 12:43pm, Maury Barbato > Kendall and Stuart in paragraph 46.9 of their > wonderful book The Advanced Theory of > Statistics > find an incredible formula to express the > arithmetic > mean of 2m+1 terms a_{-m}, a_{-m+1},...,a_m. > This formula involves only even central > differences > (the second central difference is defined as > (a_{1} - a_0) - (a_0 - a_{-1}) = (U - 2 + > U^(-1))(a_0), > where U is the shift operator, that is > U(a_k)=a_{k+1}. > The proof given by Kendall and Stuart left me > astonished, > because it is based on a merely simbolic > identity > U=exp(2*i*f), > where f is an unspecified angle. What does this > identity > mean? It seems quite absurd: U is not a number! > Do you have some idea about this? > Maury barbato > P. S. I add that the final idenity they find has > got > using a complicated trigonometric formula, and > precisely > formula (48) in the list > http://mathworld.wolfram.com/Multiple-AngleFormulas.ht ml Perhaps their presentation gives some hint that > transform theory is being applied? It seems > the transform of the shift operator U is being > expressed in terms of a complex multiplier of > the transform. Unfortunately, I don't have the book within reach. > Anyhow, Kendall and Stuart used to omit many > fundamental steps. I quote their words. Writing U = exp(2 * i * f), we find, symbolically, d^2 = exp(2 * i * f) - 2 + exp(-2 * i * f) = > = -4 * [(sin f)^2]. Then sum_{j = -m to m} a_j = sum_{j = -m to m} (U^j) a_0 > = =(1 + sum_{j = 1 to m} cos(2 * j * f)) a_0, since the terms in sin (2 * j * f) vanish, = [(sin[(2*m + 1)*f])/(sin f)] a_0. Thus (k = 2*m + 1) (sum_{j = -m to m} a_j)/ k = [sin(k * f)]/(k * sin f)] a_0 = a_0 + [(k^2 - 1)/(4*(3!))]*(d^2(a_0)) + + [(k^2 - 1)*(k^2 - 3^2)/(16*(5!))]*(d^4(a_0)) + ... > This interesting formula gives the arithmetic > average > in terms of the middle term a_0 and its central > differences. These are their original words ... and I'm quite > incredulous: the formula really works! > Is this black magic?! Maury Barbato Finally I solved the enigma: Kendall and Stuart use operator expansions! I found the answer in the http://www.actuaries.org.uk/__data/assets/pdf_file/0016/26044/0470-0480.pdf where the quoted formula and other interesting formulae (such as Stirling's Finite Difference Formula) are derived. Maury Barbato === Subject: Re: Arithmetic Mean <27847608.12789.1243160803946.JavaMail.jakarta@nitrogen.mathforum.org>, > .... Kendall and Stuart > use operator expansions! I found the answer in the http://www.actuaries.org.uk/__data/assets/pdf_file/0016/26044/0470-0480.pdf where the quoted formula and other interesting formulae > (such as Stirling's Finite Difference Formula) are > derived.... As a historical footnote, you may like to know that George Boole used such methods very effectively in his pioneering book A Treatise on the Calculus of Finite Differences, 1860, 1872. Ken Pledger. === Subject: Re: Arithmetic Mean <27847608.12789.1243160803946.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.10) Gecko/2009042315 Firefox/3.0.10,gzip(gfe),gzip(gfe) > <27847608.12789.1243160803946.JavaMail.jaka...@nitrogen.mathforum.org>, > .... Kendall and Stuart > use operator expansions! I found the answer in the >http://www.actuaries.org.uk/ data/assets/pdf file/0016/26044/0470-04... > where the quoted formula and other interesting formulae > (such as Stirling's Finite Difference Formula) are > derived.... As a historical footnote, you may like to know that George Boole > used such methods very effectively in his pioneering book A Treatise on > the Calculus of Finite Differences, 1860, 1872. nowadays this goes by the name of the umbral calculus though as mentioned it has a long history before the term was invented rota placed the theory on a much more sound footing by showing how the mappings arise from simple results on linear functionals -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: instructor's solutions manual for Advanced Engineering Mathematics 3rd ed zill posting-account=1eS-jwoAAAAELkogftljZurpHGkgAU86 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) I have the comprehensive instructor's solutions manuals in an electronic format for the following textbooks. They include full solutions to all the problems in the text, but please DO NOT POST HERE, instead send me email including the name and edition of the solutions manual u need. 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Bishop.pdf 4 ENGINEERING MECHANICS: STATICS by BEDFORD 5th. 5 Fundamentals of Physics (8th_Edition) By Halliday 6 Engineering and Chemical Thermodynamics by Wyatt Tenhaeff Milo Koretsky 7 Macroeconomics, 5E Olivier Blanchard (instructor manual) 8 Modern Physics, 2/E Randy Harris SM 9 fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SM) 10 solution manual for Separation Process Engineering: 2e by wankat SM 11 Macroeconomics, 5E Olivier Blanchard (test bank) 12 solution manual for Probability and Statistical Inference ( 7th edition by Hogg & Tanis) 13 Engineering Mechanics, Statics / Dynamics 6th by J. L. Meriam, L. G. 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Morris Mano, Michael D. Ciletti Solutions manual to Engineering and Chemical Thermodynamics by Milo D. Koretsky Solutions manual to Fundamentals of Clas Sical Thermodynamics 6th edition by Van Wylen Solutions manual to Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Solutions manual to Mechanical Vibrations, Third Edition, by Singiresu S. Rao Solutions manual to Microelectronic Circuit Analysis and Design, 3ed. by Neamen (2006) - [Solutions Manual Only] by Donald A. Neamen Solutions manual to Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Solutions manual to Modern Organic Synthesis: An Introduction by Michael H. Nantz, Hasan Palandoken, George S. Zweifel Solutions manual to Power System Analysis By John J. Grainger, William D. Stevenson Jr Solutions manual to Investments Student Solutions Manual 6e by Zvi Bodie Solutions manual to Auditing and Assurance Services 12 th by: Alvin A Arens, Randal J Elder, Mark Beasley Solutions manual to Signals and Systems: Analysis of Signals Through Linear Systems by: M.J. Roberts, M.J. Roberts === Subject: Re: A challenge to Mensanator:VMCM1905 > This challenge is now posed exclusively to Mensanator This is usenet you dumb. You cannot post exclusively to any one > person. Before calling people dumb, perhaps you should learn the difference between the verb to 'pose' and the verb to 'post'. Phil -- Marijuana is indeed a dangerous drug. It causes governments to wage war against their own people. -- Dave Seaman (sci.math, 19 Mar 2009) === Subject: Re: A challenge to Mensanator:VMCM1905 > This challenge is now posed exclusively to Mensanator > This is usenet you dumb. You cannot post exclusively to any one > person. Before calling people dumb, perhaps you should learn the > difference between the verb to 'pose' and the verb to 'post'. No change needed. I did no confused the verbs pose with post. The OP *posted* to the entire newsgroup. He then asserted that his post posed a question only to one person, therefore trying to limit the response made to only one person. This assumes moderation, which in an unmoderated newsgroup is not possible. If the jackass wanted to pose a question to only one person, the jackass should not: a. Post to an entire usenet newsgroup. b. Pose an exclusive question to more than one person. If you don't slap idiots, they stay idiots. The OP is indeed a dumb, and any other such label that is a synonym. Go elsewhere to defend the cranks, crackpots, and the dolts. === Subject: Re: Acceleration shrinks objects > Anybody who thinks the impossible is possible, like life-after-death, > time-travel, or fountain-of-youth, is the obvious dolt. He is saying > I'm too much of a moron to realize I am a moron. Ah, one more God-like being who possesses all knowledge POSSIBLE in the universe which is of course required to know that no way exists for this or that to happen. Which is why these Gods can say things he's too much of a moron to realize he's a moron for saying that a motor without a commutator is impossible, that heavier than air craft are impossible or that a fountain of youth is impossible even though any biologist can tell you that at the cellular level there is no reason that the body could not go on replacing it's cells forever. Strich, why don't you just use the short version of saying that this or that is impossible. Namely: I'm an ignorant egotistical idiot! ------------------------------------------------------------ In your case, Binj, that was never in doubt :-). > The cosmic ray observes me to be time dilated by a factor of 10. I do > not observe such time dilation on my watch, my clock or my cells. > Observation easily disproves time dilation. Ah, and you are not only a moron but a kook too! Never be smarter than Einstein that way! === Subject: Re: Acceleration shrinks objects BBC-Dangerous Knowledge (Part 1-10) http://www.youtube.com/watch?v=Cw-zNRNcF90 BBC-Dangerous Knowledge (Part 2-10) http://www.youtube.com/watch?v=wpWXT9yMBnw&feature=related BBC-Dangerous Knowledge (Part 3-10) http://www.youtube.com/watch?v=1AAvWb5wYNk&feature=related BBC-Dangerous Knowledge (Part 4-10) http://www.youtube.com/watch?v=qUL-x8Gm1h4&feature=related BBC-Dangerous Knowledge (Part 5-10) http://www.youtube.com/watch?v=So9RAbBy1ps&feature=related BBC-Dangerous Knowledge (Part 6-10) http://www.youtube.com/watch?v=fqKQ0-T3swY&feature=related BBC-Dangerous Knowledge (Part 7-10) http://www.youtube.com/watch?v=oldUAw2Aux0&feature=related BBC-Dangerous Knowledge (Part 8-10) http://www.youtube.com/watch?v=0ZcErXdR_eQ&feature=related BBC-Dangerous Knowledge (Part 9-10) http://www.youtube.com/watch?v=BkezCyb7Lkw&feature=related BBC-Dangerous Knowledge (Part 10-10) http://www.youtube.com/watch?v=_8dczB1rY-Q&feature=related -- Ahmed Ouahi, Architect Androcles kirjoitti viestiss.8a:W_aSl.20960$wz2.6397@newsfe30.ams2... > Anybody who thinks the impossible is possible, like life-after-death, > time-travel, or fountain-of-youth, is the obvious dolt. He is saying > I'm too much of a moron to realize I am a moron. Ah, one more God-like being who possesses all knowledge POSSIBLE in > the universe which is of course required to know that no way exists > for this or that to happen. Which is why these Gods can say things > he's too much of a moron to realize he's a moron for saying that a > motor without a commutator is impossible, that heavier than air craft > are impossible or that a fountain of youth is impossible even though > any biologist can tell you that at the cellular level there is no > reason that the body could not go on replacing it's cells forever. Strich, why don't you just use the short version of saying that this > or that is impossible. > Namely: I'm an ignorant egotistical idiot! > ------------------------------------------------------------ > In your case, Binj, that was never in doubt :-). > The cosmic ray observes me to be time dilated by a factor of 10. I do > not observe such time dilation on my watch, my clock or my cells. > Observation easily disproves time dilation. Ah, and you are not only a moron but a kook too! Never be smarter > than Einstein that way! === Subject: Re: Saifee Durbar: His Life, His Accomplishments, His Dreams posting-account=IogFHgoAAABYe_j3UKpn-ceHOgT_YnWx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Learn more aboutSaifeeDurbar: the man, his humble beginnings, his > accomplishments and his dreams: http://saifdurbar.wordpress.com http://saifeedurbar.wordpress.com And now, Saif Durbar will help the people of Darfur with a railway linking Cameroon, Central African Republic and Sudan. Details are on the Saifee Durbar blog: http://saifeedurbar.wordpress.com http://saifdurbar.wordpress.com === Subject: Re: Saif Durbar talks about the Sudan - Cameroon Railway > SaifDurbar: My dream, which has become a full-fledged project, is to > build a railway that will run from one end of the country to the > other. God's willing, this will be done soon. The line will go from > Cameroon to Sudan and will provide Africa with something it needs more > than ever: mobility. Transportation costs are so high that all > economic endeavours are affected by it. And now, Saif Durbar will help the people of Darfur with a railway linking Cameroon, Central African Republic and Sudan. Details are on the Saifee Durbar blog: http://saifeedurbar.wordpress.com http://saifdurbar.wordpress.com === Subject: Re: Integral brick disproof from last month? > x^2 - n y^2 = 1 has solutions in positive integers x > and y > for every positive squarefree integer n, but even for > some > moderate sized n the smallest solution is enormous. > This is > called Pell's equation. > -- > GM Hi Gerry, that's what I was looking for, it's already something but for n<13 we need only 2 digits for x and y . See http://mathworld.wolfram.com/PellEquation.html The first nearly big number for x appears for n=61. But an equation as x©Ö-61.y©Ö=1 can hardly be called a simple formulation, certainly not as simple as the integer brick formulation. Looking for solutions using brute force programming (three loops) is very quickly done w.r.t. the time that has been used for the brick problem to find NO solution. bleuprint PS: There are no solutions for n=m©Ö === Subject: Re: Integral brick disproof from last month? <32220199.12947.1243168323346.JavaMail.jakarta@nitrogen.mathforum.org>, > x^2 - n y^2 = 1 has solutions in positive integers x and y for > every positive squarefree integer n, but even for some moderate > sized n the smallest solution is enormous. This is called Pell's > equation. Hi Gerry, > that's what I was looking for, it's already something but for n<13 we need > only 2 digits for x and y . See http://mathworld.wolfram.com/PellEquation.html > > The first nearly big number for x appears for n=61. But an equation as > x©Ö-61.y©Ö=1 can hardly be called a simple formulation, certainly not as > simple as the integer brick formulation. Simplicity is in the eye of the beholder. Did I mention the congruent number problem? Given a positive, squarefree integer n, find (if it exists) a right triangle with rational sides and area n. I recommend n = 157; if you give up, try http://www.math.umd.edu/~eve/cong_num.html Oh, and stick to keyboard characters or you get weird things like the copyright symbols instead of x^2. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Ronald Federici - Internationally Recognized Adoption Therapist posting-account=PEqGZgoAAABzzUfx_T0rgrsAvdHN5jgs Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > adoption, and here is a recipe for Yorkshire Old Wives' Sodhttp://www.greenchronicle.com/regional recipes/yorkshire old wives.htm Ronald Steven Federici is often described as ñthe country's expert in the neuropsychological evaluation and treatment of children having multi-sensory neurodevelopmental impairments.î He is best described as a ñdevelopmental neuropsychologist,î specializing in the treatment of ñinstitutional autismî (which he also calls ñpost-traumatic autism,î or ñpost-institutional autistic syndromeî). Dr. Federici is licensed by the Virginia Board, and is the holder of a Psy. D. degree. Dr. Ronald Federici is the author of ñHelp for the Hopeless Child: A Guide for Families, With Special Discussion for Assessing and Treating the Post-Institutionalized Childî and is the founder of Neuropsychological and Family Practice Associates, in McLean, Virginia. He has worked with adopted children from Russia, Romania, Ukraine and Belarus. He is also the father to seven adopted children of his own. Federici is also an outspoken opponent of dangerous practices, such as those resulting in the death of Candace Newmaker. In addition, he has also sought to provide as much assistance as possible to children living in orphanages and other institutions with deplorable conditions. More information about Dr. Federici and his work can be found at: http://ronaldfederici.wordpress.com (Ronald Federici blog) http://ronfederici.wordpress.com (Ron Federici blog) http://childrenintherapy.wordpress.com (Children in Therapy) http://advocatesforchildrenintherapy.wordpress.com (Advocates for Children in Therapy) http://angelinajolieadoptions.wordpress.com (Angelina Jolie's adoptions; Dr. Federici is Angelina Jolie's adoption consultant) === Subject: Solution Manual & Test Banks in electronic format for sale posting-account=jy2E5goAAAB1WGwMQL1h2k61o4k7O_u4 Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Visit http://quick-n-easy-solution-shop.blogspot.com for a list of solution manual/ test bank for sale or here is the list: and email your requirements to emanuelu4[at]gmail.com HERE IS THE LIST OF MANUALS FOR SALE: Introductory Circuit Analysis 11e Boylestad Solution manual Mathematical Thinking problem solving Angelo & West Instructors manual ISBN -0130144126 Human Anatomy & Physiology 7E TEST BANK ISBN 0805373810 Electronic Devices and Circuit Theory 9e Instructors resource manual ISBN 0132214466 Prince Medical Imaging Signals and Systems Instructors manual Prebles' Artforms TestBank Management Information Systems Managing the Digital Firm 10th Edition by Laudon Understanding and Managing Organizational Behavior 5E Test bank Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Solution Manual & Test bank Organic Chemistry 6E Wade Test Bank Strategic Management and Competitive Advantage Concepts and Cases 2E barney hesterly ISBN 0136036112Pearson TESTGEN file Biology with Mastering Biology 8E Campbell Reece ISBN -0321494334 Test Bank Fundamentals of Differential Equations 7thE Nagle Snider Instructors resource manual ISBN -0321388445 Brock Biology of Microorganisms 12E ISBN -0132324997 Test Bank Introduction to the Design and Analysis of Algorithms 2E Levitin ISBN 0321428102 Prebles' Artforms 9E patrick Frank TESTGEN file ISBN 0136044166 International Economics Theory and Policy 8E Krugman Obstfeld Management Information Systems 11E Laudon 0136078907 test bank FriendlyIntroductionToAnalysis (2ndEd) - Kosmala [CapitalEth] SolutionsManual Fundamentals of Communication Systems Java Foundations- Introduction to Program Design and Data Structures- ES zip Object Oriented Programming in C++ 4E suplement robert Lafore Operations Management 9E Jay Heizer ISBN 0132342979 test bank Operations Management 9E Jay Heizer ISBN 0131585576 Statistics 11E James T. 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Ehrenberg (10th Ed) (ISBN-10: 032153896X) Organizational Behaviour: Concepts, Controversies, Applications - Nancy Langton (4th Ed) (ISBN-10: 0131971107) Organizational Theory, Design, and Change - Gareth R. Jones (1st Ed) (ISBN-10: 0131245228) Personal Finance for Canadians - Elliot J. Currie (9th Ed) (ISBN-10: 0132286750) Principles of Accounting - Meg Pollard (1st Ed) (ISBN-10: 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd Ed) (ISBN-10: 0273684108) Principles of Marketing Canadian Edition - Philip Kotler (7th Ed) (ISBN-10: 0132020017) Principles of Marketing European Edition - Philip Kotler (5th Ed) (ISBN-10: 0273720643) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th Ed) (ISBN-10: 0132047675) Psychology Canadian Edition - Saundra Ciccarelli (1st Ed) (ISBN-10: 0138152160) Selling Today - Gerald L. Manning (4th Ed) (ISBN-10: 0131275992) Society: The Basics Canadian Edition - John J. Macionis (4th Ed) (ISBN-10: 0132057913) Statistics for Economics, Accounting & Business Studies - Michael Barrow (5th Ed) (ISBN-10: 0273717987) Statistics: International Edition - James McClave (10th Ed) (ISBN-10: Survey of Accounting: Making Sense of Business - Katherene P. Terrell (1st Ed) (ISBN-10: 0130911844) Technical Communication Canadian Edition - William S. Pfeiffer (4th Ed) (ISBN-10: 0131962930) The Canadian Criminal Justice System - Thomas Fleming (2nd Ed) (ISBN-10: 0131992465) The Economics of Money, Banking, and Financial Markets Canadian Edition - F. S. Mishkin (3rd Ed) (ISBN-10: 032142395X) The Law and Business Administration in Canada - J. E. Smyth (11th Ed) (ISBN-10: 0132042754) The Practice of Market Research: An Introduction - Yvonne Mcgivern (3rd Ed) (ISBN-10: 0273717073) Thomas' Calculus: International Edition - George B. Thomas, Jr (11th Ed) (ISBN-10: 0321243358) Understanding Financial Statements - Lyn M. Fraser (8th Ed) (ISBN-10: 0131878565) Understanding Financial Statements: International Edition (9th Ed) (ISBN-10: 0138153272) Using QuickBooks Pro 2005 for Windows - M. Purbhoo (1st Ed) (ISBN-10: 0321243307) 2009 Corporate, Partnership, Estate and Gift Taxation - James Pratt 3rd ed ISBN - 1426639015 2009 Federal Taxation - James Pratt 3rd ed ISBN - 1426639171 2009 Individual Taxation - James Pratt 3rd ed ISBN - 1426649193 A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet - Sara Baase 3rd ed ISBN - 0136008488 Absolute C++ - Walter Savitch 3rd ed ISBN - 0321468937 Absolute Java - Walter Savitch 3rd ed ISBN - 0321487923 Access 2007 Guidebook - Maggie Trigg 6th ed ISBN - 0321517016 Accounting - Carl Warren 22nd ed ISBN - 0324401841 Accounting - Carl Warren 23rd ed ISBN - 0324662963 Accounting Chapters 1-13 - Charles T. Horngren et al 7th ed ISBN - 0132249952 Accounting Chapters 1-25 - Charles T. 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Groover 2nd ed ISBN - 0130889784 Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover 3rd ed ISBN - 0132393212 Basic Business Statistics - Mark L Berenson 10th ed ISBN - 0131678310 Basic Chemistry - Karen C. Timberlake 2nd ed ISBN - 0805344691 Basic Economics - Frank V. Mastrianna Test Bank 15th ed ISBN - 0324599161 Basic Environmental Technology: Water Supply, Waste Management & Pollution Control - Jerry A. Nathanson 5th ed ISBN - 0131190822 Basic Marketing Research Using Microsoft Excel Data Analysis - Alvin C Burns 2nd ed ISBN - 0132059584 Basic Mathematics through Applications - Geoffrey Akst 4th ed ISBN - 0321500113 Basics of Occupational Safety - David L. Goetsch 1st ed ISBN - 013502613X Beginning & Intermediate Algebra - Elayn El Martin-Gay 5th ed ISBN - 0136007317 Beginning Algebra - Elayn El Martin-Gay 5th ed ISBN - 0136007023 Beginning Algebra - Margaret L. Lial 10th ed ISBN - 0321437268 Beginning Algebra with Applications & Visualization - Gary K. Rockswold 2nd ed ISBN - 0321500040 Beginning and Intermediate Algebra - Margaret L. Lial 4th ed ISBN - 0321442334 Beginning and Intermediate Algebra with Applications & Visualization - Gary K. Rockswold 2nd ed ISBN - 0321500059 Behavior in Organizations - Jerald Greenberg 9th ed ISBN - 0131542842 Biochemistry - Mary Campbell 4th ed ISBN - 0534405215 Biochemistry with Lecture Notebook - Mary Campbell 4th ed ISBN - 0534391818 Biology - Neil A. Campbell Test Bank only w/ TestGen Software 7th ed ISBN - 080537146X Biology: Science for Life - Colleen Belk 3rd ed ISBN - 0321559592 Biology: Science for Life with Physiology - Colleen Belk 3rd ed ISBN - 0321559584 Biomaterials: The Intersection of Biology and Materials Science - Johnna S. Temenoff 1st ed ISBN - 0130097101 Biostatistics for the Health Sciences - R. Clifford Blair 1st ed ISBN - 0131176609 Bond Markets, Analysis and Strategies - Frank Fabozzi 6th ed ISBN - 0131986430 Bond Markets, Analysis, and Strategies - Frank J Fabozzi 7th ed ISBN - 0136078974 Brief Course in Mathematical Statistics - Elliot A. Tanis 1st ed ISBN - 0131751395 Brief Principles of Macroeconomics - Gregory Mankiw 5th ed ISBN - 0324590377 Brock Biology of Microorganisms - Michael T. Madigan 12th ed ISBN - 0132324601 Brock Biology of Microorganisms - Michael T. Madigan Test Bank 11th ed ISBN - 0132192268 Building Construction: Principles, Materials, and Systems - Madan Mehta 1st ed ISBN - 0130494216 Building Java Programs: A Back to Basics Approach - Stuart Reges 1st ed ISBN - 0321382838 Business - William M. Pride 10th ed ISBN - 0324829558 Business Analysis and Valuation: Using Financial Statements - Krishna Palepu 3rd ed ISBN - 0132346451 Business and Its Environment - David P. Baron 6th ed ISBN - 0136083927 Business and Society: Ethics and Stakeholder Management - Archie B. Carroll 7th ed ISBN - 0324569394 Business Communication Essentials - Courtland Bovee 4th ed ISBN - 0136084419 Business Communication Essentials and Peak Performance Grammar and Mechanics 2.0 CD Package - Court Bovee 3rd ed ISBN - 0132328992 Business Communication Today - Court Bovee 9th ed ISBN - 0131995359 Business Data Networks and Telecommunications - Raymond R. Panko 7th ed ISBN - 0136153402 Business English: Writing in the Workplace - Blanche Ettinger 4th ed ISBN - 0131565702 Business Ethics: A Stakeholder and Issues Management Approach - Joseph W. Weiss 6th ed ISBN - 0324589735 Business Ethics: Case Studies and Selected Readings - Marianne M. Jennings 6th ed ISBN - 0324657749 Business Forecasting - John Hanke 9th ed ISBN - 0132301202 Business in Action with Real Time Updates - Court Bovee 4th ed ISBN - 0136154085 Business Law - Henry R. Cheeseman 7th ed ISBN - 0136085547 Business Law and the Legal Environment - Jeffrey F. Beatty 4th ed ISBN - 0324303971 Business Law and the Legal Environment - Jeffrey F. Beatty 5th ed ISBN - 0324663528 Business Law and the Regulation of Business - Richard A. Mann 9th ed ISBN - 0324537131 Business Law Principles for Today's Commercial Environment - David P. Twomey 2nd ed ISBN - 0324303947 Business Law Today: Comprehensive - Roger LeRoy Miller 8th ed ISBN - 0324595743 Business Law Today: The Essentials - Roger LeRoy Miller 8th ed ISBN - 0324654545 Business Law: Alternate Edition - Gaylord A. Jentz 11th ed ISBN - 0324596162 Business Law: Text and Cases - Kenneth W. Clarkson 11th ed ISBN - 0324655223 Business Law: Text and Exercises - Roger LeRoy Miller 5th ed ISBN - 032464096X Business Statistics: A Decision Making Approach - David F. Groebner 7th ed ISBN - 0132416921 Business Statistics: A First Course - David Levine 5th ed ISBN - 0136065805 Business: Its Legal, Ethical, and Global Environment - Marianne M. Jennings 8th ed ISBN - 0324655541 Calculus - Dale Varberg 9th ed ISBN - 0131429248 Calculus and Its Applications - Larry Goldstein 11th ed ISBN - 0131919636 Calculus and Its Applications - Larry Goldstein 12th ed ISBN - 0321571304 Calculus and Its Applications - Marvin L. Bittinger 8th ed ISBN - 0321166396 Calculus and Its Applications - Marvin L. Bittinger 9th ed ISBN - 0321395344 Calculus Early Transcendentals - Henry Edwards 7th ed ISBN - 0131569899 Calculus for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett 11th ed ISBN - 0132328186 Calculus for the Life Sciences - Marvin L. Bittinger 1st ed ISBN - 0321279352 Calculus With Applications - Margaret L. Lial et al 8th ed ISBN - 0321228146 Calculus with Applications for the Life Sciences - Raymond N. Greenwell 1st ed ISBN - 0201745828 Calculus, Early Transcendentals - C. Henry Edwards 7th ed ISBN - 0131569899 California Real Estate Law - Theodore Gordon 7th ed ISBN - 0324654685 Capital Budgeting and Long-Term Financing Decisions - Neil Seitz 4th ed ISBN - 0324258089 Capital Markets: Institutions and Instruments - Frank J Fabozzi 4th ed ISBN - 0136026028 Cases in Management Accounting and Control Systems - Brandt Allen 4th ed ISBN - 0135704251 Chemistry - John E McMurry Test Bank only 5th ed ISBN - 0131993232 Chemistry : An Introduction to General, Organic, Biological Chemistry - Karen Timberlake 9th ed ISBN - 0805330151 Chemistry for Changing Times - John W. Hill 12th ed ISBN - 0136054498 Chemistry: An Introduction to General, Organic, & Biological Chemistry - Karen C Timberlake 10th ed ISBN - 0136019706 Civil Drafting Technology - David A. Madsen 7th ed ISBN - 0135000688 ISBN - 0534408966 CMOS Circuit Design, Layout, and Simulation - David E. Boyce et al 1st ed ISBN - 0780334167 College Accounting 1-12 - Jeffrey Slater 9th ed ISBN - 0131071696 College Accounting 1-25 - Jeffrey Slater 10th ed ISBN - 0132286386 College Accounting Chapters 1-15 - James Heintz 19th ed ISBN - 0324382499 College Accounting Chapters 1-27 - James Heintz 19th ed ISBN - 0324376162 College Accounting Chapters 1-9 - James Heintz 19th ed ISBN - 0324382480 College Accounting: A Practical Approach Canadian Edition - Jeffrey Slater 10th ed ISBN - 0132069245 College Algebra - J. S. Ratti 1st ed ISBN - 0321296443 College Algebra - Judith A. Beecher 3rd ed ISBN - 0321466071 College Algebra - Margaret L. Lial 10th ed ISBN - 0321499131 College Algebra - Mark Dugopolski 4th ed ISBN - 0321356918 College Algebra - Michael Sullivan 8th ed ISBN - 0132402866 College Algebra - Robert F. Blitzer 5th ed ISBN - 0321559835 College Algebra and Trigonometry - J. S. Ratti 1st ed ISBN - 0321296427 College Algebra and Trigonometry - Margaret L. Lial 4th ed ISBN - 0321497449 College Algebra Enhanced with Graphing Utilities - Michael Sullivan 5th ed ISBN - 0136004911 College Algebra Essentials - Michael Sullivan 8th ed ISBN - 0136154344 College Algebra: Graphs and Models with Graphing Calculator Manual Package - Marvin L. Bittinger 4th ed ISBN - 0321531922 College Geometry - David C. Kay 2nd ed ISBN - 0321046242 College Geometry: A Problem Solving Approach with Applications - Gary L. Musser 2nd ed ISBN - 0131879693 College Math for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett 11th ed ISBN - 0131572253 College Physics - Jerry D Wilson 6th ed ISBN - 0131495798 College Physics - Jerry D Wilson 7th ed ISBN - 0321571118 College Physics with Mastering Physics - Hugh Young 8th ed ISBN - 0805390707 Communicating in the Workplace - Thomas Cheesebro 1st ed ISBN - 0136136915 Communication Systems Engineering - John G. Proakis 2nd ed ISBN - 0130617938 Comparative International Accounting - Christopher Nobes 9th ed ISBN - 0273703579 Complex Variables With Applications - A. David Wunsch 3rd ed ISBN - 0201756099 Comprehensive Periodontics for the Dental Hygienist - Mea A. Weinberg 3rd ed ISBN - 0135015421 Computer Algorithms - Allen Van Gelder, Sara Baase 3rd ed ISBN - 0201612445 Computer Networking Complete Package - James F. Kurose 3rd ed ISBN - 0321418492 Computer Networking with Internet Protocols - William Stallings 1st ed ISBN - 0131410989 Computer Networking: A Top-Down Approach - James F. Kurose 4th ed ISBN - 0321497708 Computer Networking: A Top-Down Approach - James F. Kurose 5th ed ISBN - 0136079679 Computer Networking: A Top-Down Approach Featuring the Internet - James F. Kurose 3rd ed ISBN - 0321227352 Computer Organization and Architecture - William Stallings 7th ed ISBN - 0130351199 Computer Organization and Architecture: Designing for Performance - William Stallings 7th ed ISBN - 0131856448 Computer Organization and Architecture: Designing for Performance - William Stallings 8th ed ISBN - 0136073735 Computer Science: An Overview - J. Glenn Brookshear 10th ed ISBN - 0321524039 Computer Security: Principles and Practice - William Stallings 1st ed ISBN - 0136004245 Computer Systems Organization & Architecture - John D. Carpinelli 1st ed ISBN - 0201612534 Concepts in Federal Taxation 2007 - Kevin Murphy 14th ed ISBN - 0324313527 Concepts in Federal Taxation 2008 - Kevin Murphy 15th ed ISBN - 0324640153 Concepts in Federal Taxation 2009 - Kevin Murphy 16th ed ISBN - 0324659377 Concepts In Systems and Signals - John D. Sherrick 2nd ed ISBN - 0131782711 Concepts of Calculus with Applications - Martha Goshaw 1st ed ISBN - 0321320786 Concepts of Calculus With Applications-Updated Edition - Martha Goshaw 2nd ed ISBN - 0321577442 Concepts of Programming Languages - Robert W. Sebesta 8th ed ISBN - 0321493621 Conceptual Physical Science - Paul G. Hewitt 4th ed ISBN - 0321516958 Conceptual Physics Fundamentals - Paul G. Hewitt 1st ed ISBN - 0321501365 Conceptual Physics Media Update - Paul G. Hewitt 10th ed ISBN - 0321548094 Concrete Structures - Mehdi Setareh 1st ed ISBN - 0131988271 Construction Accounting & Financial Management - Stephen Peterson 2nd ed ISBN - 0135017114 Construction Methods and Management - Stephens W. Nunnally 7th ed ISBN - 0131716859 Construction Project Management - Fred Gould 3rd ed ISBN - 0131996231 Consumer Behavior - Michael Solomon 8th ed ISBN - 0136015964 Consumer Behavior - Wayne D. Hoyer 5th ed ISBN - 0547079923 Contemporary Auditing: Real Issues & Cases - Michael C. Knapp 7th ed ISBN - 0324658052 Contemporary Auditing: Real Issues & Cases Update - Michael C. Knapp 7th ed ISBN - 143907819X Contemporary Business and Online Commerce Law - Henry R. Cheeseman 6th ed ISBN - 013601500X Contemporary Engineering Economics - Chan S. Park 4th ed ISBN - 0131876287 Contemporary Financial Management - Charles Moyer 10th ed ISBN - 0324289081 Contemporary Financial Management - R. Charles Moyer, James R. McGuigan 11th ed ISBN - 0324653506 Contemporary Logistics - Paul R. Murphy 9th ed ISBN - 013156207X Contemporary Marketing - Louis E. Boone 14th ed ISBN - 032458203X Contemporary Marketing 2009 Update - Louis E. Boone 13th ed ISBN - 0324580215 Contemporary Project Management - Timothy Kloppenborg 1st ed ISBN - 0324382383 Cornerstones of Managerial Accounting - Maryanne M. Mowen 2nd ed ISBN - 0324379609 Cornerstones of Managerial Accounting - Maryanne M. Mowen 3rd ed ISBN - 0324660138 Corporate Finance - Jonathan Berk 1st ed ISBN - 0321415116 Corporate Finance - Michael C. Ehrhardt, Eugene F. Brigham 3rd ed ISBN - 0324655681 Corporate Finance: The Core plus MyFinanceLab Student Access Kit - Jonathan Berk 1st ed ISBN - 032155759X Corporate Financial Accounting - Carl S. Warren 10th ed ISBN - 0324663838 Corporate Financial Management - Douglas R. Emery 3rd ed ISBN - 0132278723 Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar 12th ed ISBN - 0131495380 Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar 13th ed ISBN - 0136126634 Cost Accounting Canadian Edition - Charles Horngren 4th ed ISBN - 0131971905 Cost Accounting: Traditions & Innovations - Jesse Barfield 5th ed ISBN - 032418090X Cost Benefit Analysis: Concepts and Practice - Anthony Boardman 3rd ed ISBN - 0131435833 Cost Management: Accounting and Control - Don R. Hansen, Maryanne M. Mowen 6th ed ISBN - 0324559674 Course in Probability - Neil Weiss 1st ed ISBN - 0201774712 Criminology: A Global Perspective - Robert W. Winslow 1st ed ISBN - 0131839020 Cryptography and Network Security - William Stallings 4th ed ISBN - 0131873164 Customer Service: Career Success Through Customer Loyalty - Paul R. Timm 4th ed ISBN - 0132236583 Data Abstraction & Problem Solving with C++ - Frank M. Carrano 5th ed ISBN - 0321433327 Data and Computer Communications - William Stallings 8th ed ISBN - 0132433109 Data Structures and Algorithm Analysis in C++ - Mark Allen Weiss 3rd ed ISBN - 032144146X Data Structures and Algorithm Analysis in Java - Mark Allen Weiss 2nd ed ISBN - 0321370139 Database Concepts - David Kroenke 3rd ed ISBN - 0131986252 Database Concepts - David Kroenke 4th ed ISBN - 0136086535 Database Systems: A Practical Approach - Thomas M. Connolly 4th ed ISBN - 0321294017 Derivatives Markets - Robert L. McDonald 2nd ed ISBN - 032128030X Detection and Estimation:Theory and Its Applications - Thomas Schonhoff 1st ed ISBN - 0130894990 Developmental Mathematics - Marvin L. Bittinger 7th ed ISBN - 0321331915 Developmental Mathematics: Basic Mathematics and Algebra - Margaret L. Lial 1st ed ISBN - 0321506421 Differential Equations - John Polking 2nd ed ISBN - 0131437380 Differential Equations and Boundary Value Problems: Computing and Modeling - Henry Edwards 4th ed ISBN - 0131561073 Differential Equations and Linear Algebra - Henry Edwards, David E. Penney 2nd ed ISBN - 0131481460 Differential Equations and Linear Algebra - Henry Edwards, David E. Penney 3rd ed ISBN - 0136054250 Differential Equations and Linear Algebra - Jerry Farlow 2nd ed ISBN - 0131860615 Differential Equations and Linear Algebra - Stephen W. Goode 3rd ed ISBN - 0130457949 Differential Equations Computing and Modeling - Henry Edwards 4th ed ISBN - 0136004385 Differential Equations With Boundary Value Problems - John C. Polking 2nd ed ISBN - 0130911062 Digital & Analog Communication Systems - Leon Couch 7th ed ISBN - 0131424920 Digital Communications - John Proakis 4th ed ISBN - 0072321113 Digital Design - Morris Mano 4th ed ISBN - 0131989243 Digital Electronics: A Practical Approach - William Kleitz 8th ed ISBN - 0132435780 Digital Fundamentals - Thomas Floyd 10th ed ISBN - 0132359235 Digital Signal Processing - John Proakis 4th ed ISBN - 0131873741 Digital Signal Processing Using MATLAB -Vinay K. Ingle, John G. Proakis 2nd ed ISBN - 0495073113 Digital Systems Design Using VHDL - Charles H. Roth 2nd ed ISBN - 0534384625 Digital Systems: Principles and Applications - Ronald Tocci et al 10th ed ISBN - 0131725793 Discrete and Combinatorial Mathematics - Ralph P. Grimaldi 5th ed ISBN - 0201726343 Discrete Mathematics - Edgar G. Goodaire, Michael M Parmenter 3rd ed ISBN - 0131679953 Discrete Mathematics - Otto, Eynden, Dossey, Spence 4th ed ISBN - 0321079124 Discrete Mathematics - Otto, Eynden, Dossey, Spence 5th ed ISBN - 0321305159 Discrete Mathematics - Richard Johnsonbaugh 6th ed ISBN - 0131176862 Drugs & the Human Body - Ken Liska 8th ed ISBN - 0132447134 Dynamics of Structures - Anil K. Chopra 3rd ed ISBN - 013156174X ECON for Macroeconomics - William A. McEachern 1st ed ISBN - 0324587805 Economic Development - Michael P. Todaro 10th ed ISBN - 0321485734 Economic Development - Michael Todaro, Stephen Smith 9th ed ISBN - 0321278887 Economic Growth - David N. Weil 2nd ed ISBN - 0321416627 Economic Growth - David Weil 1st ed ISBN - 0201680262 Economics - Michael Parkin 8th ed ISBN - 0321423003 Economics - Michael Parkin 9th ed ISBN - 0321600037 Economics - Richard Lipsey 13th ed ISBN - 0321369211 Economics - Roger A. Arnold 9th ed ISBN - 0324595425 Economics for Managers - Paul G Farnham 1st ed ISBN - 0130924253 Economics for Managers - Paul G Farnham 2nd ed ISBN - 013606552X Economics for Today - Irvin B. Tucker 6th ed ISBN - 0324591365 Economics of Money, Banking, and Financial Markets - Frederic Mishkin Test Bank 8th ed ISBN - 0321415051 Economics of Money, Banking, and Financial Markets, Update - Frederic Mishkin 7th ed ISBN - 0321331850 Economics Today - Roger LeRoy Miller 14th ed ISBN - 0321422341 Economics Today - Roger Miller 15th ed ISBN - 0321600215 Economics Today: The Macro View - Roger Miller 13th ed ISBN - 0321278992 Economics Today: The Macro View - Roger Miller 14th ed ISBN - 0321421442 Economics Today: The Macro View - Roger Miller 15th ed ISBN - 0321600223 Economics Today: The Micro View - Roger Miller 13th ed ISBN - 0321278984 Economics Today: The Micro View - Roger Miller 14th ed ISBN - 0321425065 Economics Today: The Micro View - Roger Miller 15th ed ISBN - 0321600185 Economics: A Contemporary Introduction - William A. McEachern 8th ed ISBN - 0324579217 Economics: A Tool for Critically Understanding Society - Tom Riddell 8th ed ISBN - 0321423585 Economics: Principles and Policy - William J. Baumol 10th ed ISBN - 0324537026 Economics: Principles and Policy - William J. Baumol 11th ed ISBN - 0324586205 Economics: Private and Public Choice - James D. Gwartney 12th ed ISBN - 0324580185 Effective Small Business Management - Norman M. Scarborough 9th ed ISBN - 0136152708 Effective Writing - Claire B. May 8th ed ISBN - 0136029086 Electric Circuits - James Nilsson 8th ed ISBN - 0131989251 Electrical Engineering: Principles and Applications - Allan R. Hambley 4th ed ISBN - 0131989227 Electrical Machines, Drives and Power Systems - Theodore Wildi 6th ed ISBN - 0131776916 Electronic Commerce 2008 - Efraim Turban 5th ed ISBN - 0132243318 Electronic Communications for Technicians - Tom Wheeler 2nd ed ISBN - 0131130498 Electronics and Computer Math - Bill R. Deem 8th ed ISBN - 0131711377 Electronics Fundamentals: Circuits, Devices and Applications - Thomas Floyd 7th ed ISBN - 013219709X Elementary Algebra - George Woodbury 1st ed ISBN - 0321166426 Elementary Algebra Early Graphing for College Students - Allen R. Angel 3rd ed ISBN - 0136134165 Elementary Algebra: Graphs and Authentic Applications - Jay Lehmann 1st ed ISBN - 013220164X Elementary and Intermediate Algebra - George Woodbury 2nd ed ISBN - 0321500067 Elementary and Intermediate Algebra: Graphs & Models - Marvin L. Bittinger 3rd ed ISBN - 0321422406 Elementary Differential Equations - Henry Edwards 6th ed ISBN - 0132397307 Elementary Differential Equations - Werner E. Kohler, Lee W.Johnson 1st ed ISBN - 0201709260 Elementary Differential Equations with Boundary Value Problems - Henry Edwards 6th ed ISBN - 0136006132 Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al 1st ed ISBN - 0321121643 Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al 2nd ed ISBN - 0321398505 Elementary Linear Algebra - Ron Larson 6th ed ISBN - 0618783768 Elementary Linear Algebra with Applications - Bernard Kolman 9th ed ISBN - 0132296543 Elementary Number Theory - Kenneth H. Rosen 5th ed ISBN - 0321237072 Elementary Statistics - Mario F. Triola 10th ed ISBN - 0321331834 Elementary Statistics - Mario F. Triola 9th ed ISBN - 0201775700 Elementary Statistics - Mario F. Triola 11th ed ISBN - 0321500245 Elementary Statistics - Neil A. Weiss 7th ed ISBN - 0321422090 Elementary Statistics - Ron Larson 4th ed ISBN - 0132424339 Elementary Statistics Using Excel - Mario Triola 3rd ed ISBN - 0321365135 Elementary Statistics Using the TI-83/84 Plus Calculator - Mario F. Triola 2nd ed ISBN - 0321462572 Elementary Statistics With Multimedia Study Guide - Mario F. Triola 10th ed ISBN - 0321460928 Elements of Forecasting - Francis X. Diebold 4th ed ISBN - 032432359X Embedded Microcontrollers & Processor Design - Charles Greg Osborn 1st ed ISBN - 0131130412 Embedded System Design with C805 - Han-Way Huang 1st ed ISBN - 0495471747 Employment Law - John J. Moran 4th ed ISBN - 0136009964 Engineering Computation with MATLAB - David M. Smith 2nd ed ISBN - 0136080634 Engineering Economy - William G Sullivan 13th ed ISBN - 0131486497 Engineering Economy - William G. Sullivan 14th ed ISBN - 0136142974 Engineering Economy and the Decision-Making Process - Joseph C. Hartman 1st ed ISBN - 0131424017 Engineering Fundamentals: An Introduction to Engineering - Saeed Moaveni 3rd ed ISBN - 0495082538 Engineering Materials: Properties and Selection - Ken Budinski 8th ed ISBN - 0131837796 Engineering Materials: Properties and Selection - Kenneth G. Budinski 9th ed ISBN - 0137128428 Engineering Mechanics Dynamics - Anthony M Bedford 5th ed ISBN - 0136129161 Engineering Mechanics: Dynamics - Andrew Pytel 3rd ed ISBN - 0495295612 Engineering Mechanics: Statics - Andrew Pytel 3rd ed ISBN - 0495244694 Engineering Mechanics: Statics - Anthony M Bedford 5th ed ISBN - 0136129153 Engineering Mechanics: Statics - Russell C. Hibbeler 11th ed ISBN - 0132215004 Engineering Mechanics: Statics - Russell C. Hibbeler 12th ed ISBN - 0136077900 Engineering Mechanics: Statics Computational Edition - Robert W. Soutas-Little 1st ed ISBN - 0534549217 Engineering Vibration - Daniel Inman 3rd ed ISBN - 0132281732 Enterprise Systems for Management - Luvai Motiwalla 1st ed ISBN - 013233531X Entrepreneurial Finance - Chris Leach 3rd ed ISBN - 0324561253 Entrepreneurial Finance - Philip J. Adelman 4th ed ISBN - 0132434792 Entrepreneurial Finance - Philip J. Adelman 5th ed ISBN - 013502529X Entrepreneurship: Successfully Launching New Ventures - Bruce Barringer 2nd ed ISBN - 0132240572 Entrepreneurship: Theory, Process, and Practice - Donald F. Kuratko 8th ed ISBN - 0324590911 Environmental and Natural Resource Economics - Tom Tietenberg 7th ed ISBN - 0321305043 Environmental Issues: An Introduction to Sustainability - Robert L. McConnell 3rd ed ISBN - 0131566504 Environmental Law - Nancy K. Kubasek 6th ed ISBN - 0136142168 Environmental Science: Toward A Sustainable Future - Richard T. Wright 10th ed ISBN - 0132302659 Error Control Coding - Daniel J. Costello Jr., Shu Lin 2nd ed ISBN - 0130426725 Essential Foundations of Economics - Robin Bade 4th ed ISBN - 0321522354 Essentials of Business Law - Jeffrey F. Beatty 3rd ed ISBN - 0324537123 Essentials of Business Law and the Legal Environment - Richard A. Mann 10th ed ISBN - 0324593562 Essentials of College Algebra with Modeling and Visualization - Gary K. Rockswold 3rd ed ISBN - 0321448898 Essentials of College Algebra, Alternate Edition - Margaret L. Lial 1st ed ISBN - 0321491858 Essentials of Economics - Gregory Mankiw 4th ed ISBN - 0324236964 Essentials of Economics - Gregory Mankiw 5th ed ISBN - 0324590024 Essentials of Entrepreneurship and Small Business Management - Thomas W Zimmerer 5th ed ISBN - 0132294389 Essentials of Logic - Irving Copi 2nd ed ISBN - 013238034X Essentials of Management Information Systems - Jane Laudon 8th ed ISBN - 013602579X Essentials of Managerial Finance - Scott Besley 13th ed ISBN - 0324258755 Essentials of Marketing - Charles W. Lamb 6th ed ISBN - 0324656203 Essentials of Materials Science & Engineering - Donald R. Askeland 2nd ed ISBN - 0495244465 Essentials of Organizational Behavior - Stephen P Robbins 9th ed ISBN - 0132431521 Essentials of Organizational Behavior - Stephen P. Robbins 10th ed ISBN - 0136077617 Essentials of Statistics - Mario F. Triola 3rd ed ISBN - 0321434250 Essentials of the Legal Environment - Roger LeRoy Miller 2nd ed ISBN - 0324400403 Ethics for the Information Age - Mike Quinn 3rd ed ISBN - 0321536851 Excellence in Business Communication - John V. Thill 8th ed ISBN - 0136157505 Experiencing MIS - David Kroenke 2nd ed ISBN - 0136078680 Exploring Business - Karen Collins 1st ed ISBN - 0131403656 Exploring Corporate Strategy - Gerry Johnson 8th ed ISBN - 140588732X Exploring Macroeconomics - Robert L. Sexton 4th ed ISBN - 0324395558 Federal Tax Research - William A. Raabe 8th ed ISBN - 0324659652 Feedback Control of Dynamic Systems - Gene Franklin 5th ed ISBN - 0131499300 Financial & Managerial Accounting - Carl S. Warren 9th ed ISBN - 0324401884 Financial & Managerial Accounting - Carl S. Warren 10th ed ISBN - 0324663811 Financial Accounting - Belverd E. Needles 10th ed ISBN - 0547193289 Financial Accounting - Carl S. Warren, James M. Reeve 10th ed ISBN - 0324380674 Financial Accounting - Carl S. Warren, James M. Reeve 11th ed ISBN - 0324663781 Financial Accounting - Jane Reimers 1st ed ISBN - 0131492012 Financial Accounting - Walter Harrison, Charles Horngren 6th ed ISBN - 0131499459 Financial Accounting - Walter Harrison, Charles Horngren 7th ed ISBN - 0138128200 Financial Accounting and Financial Tips - Walter T. Harrison 7th ed ISBN - 0135012848 Financial Accounting, Reporting & Analysis: International Edition - Barry Elliott 2nd ed ISBN - 027370253X Financial Accounting: A Bridge to Decision Making - Robert Ingram 6th ed ISBN - 0324313357 Financial Accounting: A Business Process Approach - Jane L. Reimers 2nd ed ISBN - 0131473867 Financial Accounting: An Integrated Statements Approach - Jonathan Duchac 2nd ed ISBN - 0324312113 Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney 12th ed ISBN - 0324381980 Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney 13th ed ISBN - 0324651147 Financial Accounting: The Impact on Decision Makers - Gary Porter 6th ed ISBN - 0324655231 Financial and Managerial Accounting - Meg Pollard 1st ed ISBN - 0136008984 Financial And Managerial Accounting Ch 1-13 - Charles Horngren 1st ed ISBN - 0135009855 Financial Economics - Zvi Bodie 2nd ed ISBN - 0131856154 Financial Management for Public, Health, and Not-for-Profit - Steven A Finkler 3rd ed ISBN - 0136070736 Financial Management For Public, Health, and Not-for-Profit Organizations - Steven Finkler 2nd ed ISBN - 0131471988 Financial Management: Theory & Practice - Eugene Brigham 12th ed ISBN - 0324422695 Financial Markets and Institutions - Frederic S. Mishkin 5th ed ISBN - 0321280296 Financial Markets and Institutions - Frederic S. Mishkin 6th ed ISBN - 0321374215 Financial Markets and Institutions - Jeff Madura 8th ed ISBN - 0324568215 Financial Markets and Institutions Abridged Edition - Jeff Madura 8th ed ISBN - 0324593643 Financial Reporting and Analysis - Lawrence Revsine 3rd ed ISBN - 0131430211 Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson 10th ed ISBN - 0324304455 Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson 11th ed ISBN - 0324657420 Financial Reporting, Financial Statement Analysis, and Valuation - Clyde P. Stickney 6th ed ISBN - 0324302959 Financial/Managerial Accounting - Walter T. Harrison 1st ed ISBN - 0131568779 Finite Element Analysis Theory and Application with ANSYS - Saeed Moaveni 3rd ed ISBN - 0131890808 Finite Math and Its Application - Larry Goldstein 9th ed ISBN - 0131873644 Finite Mathematics - Margaret L. Lial et al 8th ed ISBN - 032122826X Finite Mathematics and Calculus with Applications - Margaret Lial 8th ed ISBN - 0321426517 Finite Mathematics for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett 11th ed ISBN - 0132255707 Finite Mathematics with Applications - Margaret L. Lial 9th ed ISBN - 0321386728 First Course in Abstract Algebra - John Fraleigh 7th ed ISBN - 0201763907 First Course in Abstract Algebra - Joseph Rotman 3rd ed ISBN - 0131862677 First Course In Probability - Sheldon M. Ross 7th ed ISBN - 0131856626 First Course In Probability - Sheldon M. Ross 8th ed ISBN - 013603313X First Course in Statistics, A - James T. McClave 10th ed ISBN - 0136152597 Fluency with Information Technology: Skills, Concepts, and Capabilities - Lawrence Snyder 3rd ed ISBN - 0321512391 Foundations of Economics - Robin Bade 4th ed ISBN - 0321522362 Foundations of Finance - Arthur Keown, William Petty, John Martin, David Scott 5th ed ISBN - 0131856057 Foundations of Finance: Logic and Practice of Financial Mangement - Arthur J. Keown 6th ed ISBN - 0135048168 Foundations of Finance: The Logic and Practice of Financial Management - Arthur Keown 6th ed ISBN - 0132339226 Foundations of Financial Markets and Institutions - Frank J. Fabozzi 4th ed ISBN - 0136135315 Foundations of Geometry - Gerard Venema 5th ed ISBN - 0131437003 Foundations of Macroeconomics - Robin Bade 4th ed ISBN - 0321522370 Foundations of MEMS - Chang Liu 1st ed ISBN - 0131472860 Foundations of Microeconomics - Robin Bade 3rd ed ISBN - 0321415957 Foundations of Microeconomics - Robin Bade 4th ed ISBN - 0321522389 Foundations of the Legal Environment of Business - Marianne M. Jennings 1st ed ISBN - 0324566514 Framework for Human Resource Management, A - Gary Dessler 5th ed ISBN - 0136041531 Framework for Marketing Management, A - Philip Kotler 4th ed ISBN - 0136026605 Fraud Examination - Steve Albrecht 2nd ed ISBN - 0324651155 Friendly Introduction to Analysis - Witold A.J. Kosmala 2nd ed ISBN - 0130457965 Fundamental Cornerstones of Managerial Accounting - Dan L. Heitger, Maryanne M. Mowen 1st ed ISBN - 0324378068 Fundamental Mathematics through Applications - Geoffrey Akst 4th ed ISBN - 0321496906 Fundamentals of Advanced Accounting - Paul M. Fischer Test Bank 1st ed ISBN - 0324378904 Fundamentals of Applied Electromagnetics - Fawwaz T. Ulaby 5th ed ISBN - 0132413264 Fundamentals of Business Law Summarized Cases - Roger LeRoy Miller 7th ed ISBN - 0324381689 Fundamentals of Business Law: Excerpted Cases - Roger LeRoy Miller 2nd ed ISBN - 0324595727 Fundamentals of Business Law: Summarized Cases - Roger LeRoy Miller 8th ed ISBN - 0324595735 Fundamentals of Communication Systems - John G. Proakis 1st ed ISBN - 013147135X Fundamentals of Complex Analysis - Edward Saff 3rd ed ISBN - 0139078746 Fundamentals of Derivatives Markets - Robert L. McDonald 1st ed ISBN - 0321357175 Fundamentals of Differential Equations - Kent Nagle, Edward Saff 6th ed ISBN - 0321145720 Fundamentals of Differential Equations - R. Kent Nagle 7th ed ISBN - 0321410483 Fundamentals of Differential Equations with Boundary Value Problems - R. Kent Nagle 5th ed ISBN - 0321419219 Fundamentals of Electromagnetics for Electrical and Computer Engineering - Nannapaneni Narayana Rao 1st ed ISBN - 0136013333 Fundamentals of Engineering Economics - Chan S. Park 2nd ed ISBN - 0132209608 Fundamentals of Financial Management - Eugene Brigham 11th ed ISBN - 0324319800 Fundamentals of Financial Management - Eugene F. Brigham 12th ed ISBN - 0324597703 Fundamentals of Financial Management Concise - Eugene F. Brigham 6th ed ISBN - 0324664559 Fundamentals of Investing - Lawrence J. Gitman 10th ed ISBN - 0321489381 Fundamentals of Management: Essential Concepts and Applications - Stephen P. Robbins Test Bank 5th ed ISBN - 0131487361 Fundamentals of Multinational Finance - Michael Moffett 3rd ed ISBN - 0321541642 Fundamentals of Organic Chemistry - John McMurry Test Bank only 5th ed ISBN - 0534395732 Fundamentals of Probability, with Stochastic Processes - Saeed Ghahramani 3rd ed ISBN - 0131453408 Fundamentals of Signals and Systems - Edward Kamen 3rd ed ISBN - 0131687379 Fundamentals of Statistics - Michael Sullivan 2nd ed ISBN - 0131569872 Further Mathematics for Economic Analysis - Knut Sydsaeter et al 1st ed ISBN - 0273655760 Geometry: Theorems and Constructions - Allan Berele 1st ed ISBN - 0130871214 Global Investments - Bruno Solnik 6th ed ISBN - 0321527704 Global Strategy - Mike W. Peng 2nd ed ISBN - 0324590997 Governmental and Nonprofit Accounting: Theory and Practice - Robert J. Freeman 9th ed ISBN - 0136029515 Health Economics - Charles E. Phelps 4th ed ISBN - 0321594576 High-Speed Networks and Internets: Performance and Quality of Service - William Stallings 2nd ed ISBN - 0130322210 Historical Geology - Reed Wicander 6th ed ISBN - 0495560073 Human Anatomy & Physiology - Elaine N. Marieb 7th ed ISBN - 0805359095 Human Anatomy and Physiology - Elaine N. Marieb 8th ed ISBN - 0805395911 Human Anatomy and Physiology Lab Manual - Elaine N. Marieb 9th ed ISBN - 0805372652 Human Biology: Concepts and Current Issues - Michael D. Johnson 5th ed ISBN - 0321570200 Human Diseases: A Systemic Approach - Mark Zelman 7th ed ISBN - 0135155568 Human Physiology: An Integrated Approach - Dee Unglaub Silverthorn 5th ed ISBN - 0321559398 ISBN - 0495014850 Human Relations for Career and Personal Success: Concepts, Applications, and Skills - Andrew J. DuBrin 8th ed ISBN - 0131791796 Human Relations: Interpersonal Job-Oriented Skills - Andrew J. DuBrin 10th ed ISBN - 0135019443 Human Resource Management - Gary Dessler 11th ed ISBN - 0131746170 Human Resource Management - R. Wayne Mondy 11th ed ISBN - 0136077285 Human Resource Management - Wayne Mondy 10th ed ISBN - 0132225956 Human Side of Organizations - Michael Drafke 10th ed ISBN - 0135139740 Hydrology and Floodplain Analysis - Philip B. Bedient 4th ed ISBN - 0131745891 Income Tax Fundamentals 2006 - Gerald E. Whittenburg 24th ed ISBN - 0324399022 Income Tax Fundamentals 2007 - Gerald E. Whittenburg 25th ed ISBN - 032439926X Income Tax Fundamentals 2009 - Gerald E. Whittenburg 27th ed ISBN - 0324663676 Information Systems Today: Managing in the Digital World - Leonard Jessup 3rd ed ISBN - 0132335069 Information Systems Today: Managing the Digital World - Joseph Valacich 4th ed ISBN - 0136078400 Information Technology Auditing and Assurance - James Hall 2nd ed ISBN - 0324191987 Inquiry into Physics - Vern J. Ostdiek 6th ed ISBN - 0495119431 Integrated Arithmetic and Basic Algebra - Bill E. Jordan 4th ed ISBN - 0321442555 Intel Micro 8086 - Barry B. Brey 8th ed ISBN - 0135026458 Intel Microprocessors - Barry B. Brey 7th ed ISBN - 0131195069 Intel Microprocessors - Barry B. Brey 8th ed ISBN - 0135026458 Interactive Computer Graphics: A Top-Down Approach Using OpenGL - Edward Angel 5th ed ISBN - 0321535863 Interactive Statistics - Martha Aliaga, Brenda Gunderson 3rd ed ISBN - 0131497561 Intermediate Accounting - James D. Stice 16th ed ISBN - 0324312148 Intermediate Accounting - James D. Stice 17th ed ISBN - 032459237X Intermediate Accounting - Loren A. Nikolai 10th ed ISBN - 0324651929 Intermediate Accounting - Loren A. Nikolai 11th ed ISBN - 032465913X Intermediate Accounting Revised - David Spiceland 4th ed ISBN - 0073215422 Intermediate Algebra - Elayn El Martin-Gay 5th ed ISBN - 0136007295 Intermediate Algebra - Margaret L. Lial 10th ed ISBN - 0321443624 Intermediate Algebra - Margaret L. Lial 9th ed ISBN - 0321574974 Intermediate Algebra - Marvin L. Bittinger 10th ed ISBN - 0321319087 Intermediate Algebra for College Students - Allen R. Angel 7th ed ISBN - 0132383578 Intermediate Algebra for College Students - Robert F. Blitzer 5th ed ISBN - 0136007627 Intermediate Algebra with Applications & Visualization - Gary K. Rockswold 3rd ed ISBN - 0321500032 Intermediate Algebra: Functions & Authentic Applications - Jay Lehmann 3rd ed ISBN - 0131953338 Intermediate Algebra: Graphs & Models - Marvin L. Bittinger 3rd ed ISBN - 0321416163 Intermediate Financial Management - Eugene F. Brigham 10th ed ISBN - 0324594690 International Accounting - Frederick Choi 5th ed ISBN - 0131480979 International Accounting - Frederick D. Choi 6th ed ISBN - 0131588141 International Business - John Daniels 12th ed ISBN - 0136029655 International Business - Ricky Griffin 6th ed ISBN - 0137153732 International Business Law - Ray A. August 5th ed ISBN - 013600864X International Business Law and Its Environment - Richard Schaffer 7th ed ISBN - 0324649673 International Business: Environments and Operations - John Daniels 11th ed ISBN - 0131869426 International Business: Strategy, Management, and the New Realities - Tamer Cavusgil 1st ed ISBN - 0131738607 International Business: The Challenges of Globalization - John J. Wild 4th ed ISBN - 0131747436 International Business: The Challenges of Globalization - John J. Wild 5th ed ISBN - 0137153759 International Economics - Charles Sawyer, Richard Sprinkle 2nd ed ISBN - 0131704168 International Economics - James Gerber 3rd ed ISBN - 032123796X International Economics - James Gerber 4th ed ISBN - 0321415558 International Economics - Robert Carbaugh 11th ed ISBN - 032442194X International Economics - W. Charles Sawyer 3rd ed ISBN - 0136054692 International Economics: Theory And Policy - Paul Krugman, Maurice Obstfeld 7th ed ISBN - 0321293835 International Economics: Theory and Policy - Paul R. Krugman 8th ed ISBN - 0321488830 International Financial Management - Geert Bekaert 1st ed ISBN - 0131163604 International Financial Management - Jeff Madura 9th ed ISBN - 0324568193 International Financial Management Abridged Edition - Jeff Madura 9th ed ISBN - 0324593473 International Financial Management, Abridged Edition - Jeff Madura 8th ed ISBN - 0324365632 International Management: Managing Across Borders and Cultures - Helen Deresky 6th ed ISBN - 0136143261 International Money and Finance - Michael Melvin 7th ed ISBN - 0201770288 Intro Stats - Richard D. De Veaux 3rd ed ISBN - 0321500458 Introduction to Abstract Algebra - Olympia Nicodemi 1st ed ISBN - 0131019635 Introduction to Analysis - William R. Wade 3rd ed ISBN - 0131453335 Introduction to Business Law - Jeffrey F. Beatty 2nd ed ISBN - 0324311427 Introduction to Business Statistics - Ronald M. Weiers 6th ed ISBN - 0324381433 Introduction to C++ EXCEL MATLAB & Basic Engineering Numerical Methods - Harvey G. Stenger 1st ed ISBN - 0136142931 Introduction to C++, Excel MatLab & Basic Engineering Numerical Methods - Harvey Stenger 1st ed ISBN - 0136120245 Introduction to Chemical Principles - Stephen Stoker 9th ed ISBN - 0132379945 Introduction to Computing Systems - Sanjay J. Patel, Yale Patt 2nd ed ISBN - 0072467509 Introduction to Corporate Finance - William L. Megginson 1st ed ISBN - 0324379862 Introduction to Corporate Finance - William L. Megginson 2nd ed ISBN - 0324657935 Introduction to Cryptography with Coding Theory - Wade Trappe 2nd ed ISBN - 0131862391 Introduction to Derivatives and Risk Management - Don M. Chance 7th ed ISBN - 0324321392 Introduction to Econometrics - James H. Stock 2nd ed ISBN - 0321278879 Introduction to Econometrics Brief Edition - James H. Stock 1st ed ISBN - 0321432517 Introduction to Economic Reasoning - William D. Rohlf 7th ed ISBN - 0321416112 Introduction to Electrodynamics -David J. Griffiths 3rd ed ISBN - 013805326X Introduction to Embedded Systems - Jonathan W. Valvano 1st ed ISBN - 049541137X Introduction to Environmental Engineering - P. Aarne Vesilind 3rd ed ISBN - 0495295833 Introduction to Environmental Engineering - Richard O. Mines 1st ed ISBN - 0132347474 Introduction to Environmental Engineering and Science - Gilbert M. Masters 3rd ed ISBN - 0131481932 Introduction to Financial Accounting - Charles Horngren 9th ed ISBN - 0131479725 Introduction to Fire Prevention - James C. Robertson 7th ed ISBN - 0135041945 Introduction to Fourier Optics - Joseph Goodman 3rd ed ISBN - 0974707724 Introduction to Government and Non-for-Profit Accounting - Martin Ives 6th ed ISBN - 0132366355 Introduction to Graph Theory - Douglas West 2nd ed ISBN - 0130144002 Introduction to Law - Joanne Hames 3rd ed ISBN - 0131183818 Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold 5th ed ISBN - 0201658593 Introduction to Linear Programming - Leonid Vaserstein 1st ed ISBN - 0130359173 Introduction to Management Accounting - Charles T. Horngren 14th ed ISBN - 0136129218 Introduction to Management Accounting, Chap. 1-17: International Edition - Charles Horngren 13th ed ISBN - 0131273078 Introduction to Management Science and Student - Bernard Taylor 8th ed ISBN - 0131050524 Introduction to Management Science and Student - Bernard Taylor 9th ed ISBN - 0131888099 Introduction to Materials Management - Tony Arnold 6th ed ISBN - 0132337614 Introduction to Materials Science for Engineers - James F. Shackelford 7th ed ISBN - 0136012604 Introduction to Mathematical Statistics and Its Applications - Richard J. Larsen 4th ed ISBN - 0131867938 Introduction to Operations and Supply Chain Management - Cecil Bozarth 2nd ed ISBN - 0131791036 Introduction to Optics - Frank Pedrotti et al. 3rd ed ISBN - 0131499335 Introduction to Programming with C++ - Y. Daniel Liang 2nd ed ISBN - 0136097200 Introduction to Quantum Mechanics - David Griffiths 2nd ed ISBN - 0131118927 Introduction to Risk Management and Insurance - Mark Dorfman 8th ed ISBN - 0131449583 Introduction to Risk Management and Insurance - Mark S. Dorfman 9th ed ISBN - 0132242273 Introduction to Signal and System Analysis - Kaliappan Gopalan 1st ed ISBN - 0534466060 Introduction to Spectroscopy - Donald L. Pavia 4th ed ISBN - 0495114782 Introduction to Technical Mathematics - Allyn J. Washington, Mario Triola 5th ed ISBN - 0321374177 Introduction to Telecommunications - Martha Rosengrant 2nd ed ISBN - 0131126156 Introduction to the Design & Analysis of Experiments - George C Canavos 1st ed ISBN - 0136158633 Introduction to the Design and Analysis of Algorithms - Anany Levitin 1st ed ISBN - 0201743957 Introduction to the Design and Analysis of Algorithms - Anany Levitin 2nd ed ISBN - 0321358287 Introduction to Transportation Engineering - Lester A. Hoel 1st ed ISBN - 0534952895 Introduction to Vacuum Technology - David M. Hata 1st ed ISBN - 0130450189 Introductory & Intermediate Algebra for College Students - Robert F. Blitzer 3rd ed ISBN - 0136028950 Introductory Algebra - Marvin L. Bittinger 10th ed ISBN - 0321269470 Introductory Algebra for College Students - Robert F. Blitzer 5th ed ISBN - 0132356791 Introductory Algebra through Applications - Geoffrey Akst 2nd ed ISBN - 0321518020 Introductory and Intermediate Algebra - Robert F Blitzer 2nd ed ISBN - 0131492594 Introductory Chemistry - Nivaldo J. Tro 3rd ed ISBN - 0136003826 Introductory Chemistry - Steve Russo, Michael Silver, Mike Silver 2nd ed ISBN - 032104634X Introductory Circuit Analysis - Robert Boylestad 11th ed ISBN - 0131730444 Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge 3rd ed ISBN - 0324289782 Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge 4th ed ISBN - 0324581629 Introductory Linear Algebra: An Applied First Course - Bernard Kolman 8th ed ISBN - 0131437402 Introductory Mathematical Analysis - Ernest F Haeussler 12th ed ISBN - 0132404222 Introductory Statistics - Neil A. Weiss 8th ed ISBN - 0321393619 Inventing Entrepreneurs: Technology Innovators and their Entrepreneurial Journey - Gerry George 1st ed ISBN - 0131574701 Investments - Frank K. Reilly 7th ed ISBN - 0324288999 Investments: An Introduction - Herbert B. Mayo 9th ed ISBN - 0324561261 Java Software Solutions: Foundations of Program Design - John Lewis 5th ed ISBN - 0321409493 Java: Introduction to Problem Solving and Programming - Walter Savitch 6th ed ISBN - 0136072259 John E. Freund's Mathematical Statistics with Applications - Irwin Miller 7th ed ISBN - 0131427067 Kleppner's Advertising Procedure - Ronald Lane 17th ed ISBN - 0132308290 Labor and Employment Law: Text & Cases - David Twomey 14th ed ISBN - 0324594844 Labor Relations - Arthur A Sloane 12th ed ISBN - 013196223X Labor Relations - Arthur A. Sloane 13th ed ISBN - 0136077188 Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell 8th ed ISBN - 0131868721 Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell 9th ed ISBN - 0136084354 Lakeside Company: Case Studies in Auditing - John M. Trussel 11th ed ISBN - 0131588516 Law and Economics - Robert Cooter 5th ed ISBN - 0321336348 Law and Ethics in the Business Environment - Terry Halbert 6th ed ISBN - 0324657323 Law for Business - John D. Ashcroft 16th ed ISBN - 0324381573 Leadership - Robert N. Lussier 3rd ed ISBN - 0324316976 Leadership in Organizations - Gary Yukl 7th ed ISBN - 0132424312 Learning Microsoft Office Accounting 2007 and Student CD Package - Terri Brunsdon 1st ed ISBN - 0131586602 Learning Peachtree Complete 2007 & Peachtree Complete CD Package - Terri Brunsdon 1st ed ISBN - 0132405571 Learning Quickbooks Pro 2007 and Student CD Package - Terri Brunsdon 1st ed ISBN - 0132419386 Legal Aspects of Architecture, Engineering & the Construction Process - Justin Sweet 8th ed ISBN - 0495411213 Legal Terminology - Gordon W. Brown 5th ed ISBN - 0131568043 Level Three Leadership: Getting Below the Surface - James G Clawson 4th ed ISBN - 0132423847 Linear Algebra and Its Applications - David C. Lay 3rd ed ISBN - 0321287134 Linear Algebra for Engineers and Scientists Using Matlab - Kenneth Hardy 1st ed ISBN - 0139067280 Linear Algebra with Applications - Otto Bretscher 3rd ed ISBN - 0131453343 Linear Algebra with Applications - Steven Leon 7th ed ISBN - 0131857851 Logic and Computer Design Fundamentals - M. Morris Mano 4th ed ISBN - 013198926X Machine Design: An Integrated Approach - Robert L. Norton 3rd ed ISBN - 0131481908 Machines and Mechanisms: Applied Kinematic Analysis - David H. Myszka 3rd ed ISBN - 0131837761 Macroeconomics - Andrew B. Abel 6th ed ISBN - 0321451406 Macroeconomics - Glenn Hubbard 2nd ed ISBN - 0132356694 Macroeconomics - Michael Parkin 7th ed ISBN - 032124608X Macroeconomics - Michael Parkin 8th ed ISBN - 0321416570 Macroeconomics - Michael Parkin 9th ed ISBN - 0321600053 Macroeconomics - Olivier Blanchard 5th ed ISBN - 0132078295 Macroeconomics - Richard Froyen 8th ed ISBN - 0131435825 Macroeconomics - Richard G. Lipsey 13th ed ISBN - 0321369238 Macroeconomics - Richard T Froyen 9th ed ISBN - 0132438356 Macroeconomics - Robert Gordon 10th ed ISBN - 0321278801 Macroeconomics - Robert Gordon 11th ed ISBN - 0321485513 Macroeconomics - Roger A. Arnold 9th ed ISBN - 032478550X Macroeconomics - Stephen D. Williamson 3rd ed ISBN - 0321416589 Macroeconomics: A Modern Approach - Robert J. Barro 1st ed ISBN - 0324178107 Macroeconomics: Principles and Policy - William J. Baumol 10th ed ISBN - 0324537034 Macroeconomics: Principles and Policy - William J. Baumol 11th ed ISBN - 0324586213 Macroeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin 4th ed ISBN - 0131536184 Macroeconomics: Principles, Applications, and Tools - Arthur O'Sullivan 5th ed ISBN - 013232928X Macroeconomics: Public and Private Choice - James D. Gwartney 12th ed ISBN - 0324580193 Making Career Decisions that Count: A Practical Guide - Darrell A. Luzzo 3rd ed ISBN - 0131712772 Making the Team - Leigh Thompson 3rd ed ISBN - 0131861352 Management - Michael Hitt 2nd ed ISBN - 0132354373 Management - Richard L. Daft 9th ed ISBN - 0324595840 Management - Stephen P Robbins 9th ed ISBN - 0132257734 Management Communication: A Case-Analysis Approach - James S O'Rourke 4th ed ISBN - 0136079768 Management Information Systems - Ken Laudon 11th ed ISBN - 013607846X Management of Organizational Behavior - Paul H Hersey 9th ed ISBN - 0131441396 Manager's Bookshelf - Jon L. Pierce 8th ed ISBN - 0132301652 Managerial Accounting - Carl Warren 9th ed ISBN - 0324381913 Managerial Accounting - Carl Warren 10th ed ISBN - 032466382X Managerial Accounting - Linda S. Bamber 1st ed ISBN - 0138129711 Managerial Accounting Class Test Edition - Linda S. Bamber 1st ed ISBN - 0132284634 Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers 4th ed ISBN - 0324650647 Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers 5th ed ISBN - 0324663854 Managerial Accounting: An Introduction to Concepts, Methods and Uses - Michael W. Maher 10th ed ISBN - 0324639767 Managerial Economics - Mark Hirschey 12th ed ISBN - 0324584849 Managerial Economics: A Problem Solving Approach - Luke M. Froeb 1st ed ISBN - 0324359810 Managerial Economics: Applications, Strategies, and Tactics - James R. McGuigan 11th ed ISBN - 0324421605 Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat 5th ed ISBN - 0131860151 Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat 6th ed ISBN - 0136040047 Managerial Statistics A Case-Based Approach - Peter Klibanoff 1st ed ISBN - 0324226454 Managers and the Legal Environment - Constance E. Bagley 6th ed ISBN - 0324582048 Managing Human Resources - Luis Gomez-Mejia 5th ed ISBN - 013187067X Managing in a Global Economy: Demystifying International Macroeconomics - John E. Marthinsen 1st ed ISBN - 0324395507 Managing Information Technology - Carol V Brown 6th ed ISBN - 0131789546 Managing the Law: The Legal Aspects of Doing Business - Mitchell McInnes 2nd ed ISBN - 0132042762 Manual Auditing and Assurance Practice Set: CAST - Frank A. Buckless 1st ed ISBN - 0130464716 Manufacturing Processes for Engineering Materials - Serope Kalpakjian 5th ed ISBN - 0132272717 Manufacturing, Engineering & Technology - Serope Kalpakjian 5th ed ISBN - 0131489658 Market Regulation - Roger Sherman 1st ed ISBN - 0321322320 Market-Based Management - Roger Best 5th ed ISBN - 0132336537 Marketing - Charles W. Lamb 10th ed ISBN - 0324591098 Marketing - William M. Pride 15th ed ISBN - 0547167474 Marketing Management - Dawn Iacobucci 1st ed ISBN - 0324784430 Marketing Management - Philip Kotler 13th ed ISBN - 0136009980 Materials Science and Engineering: An Introduction - William Callister 6th ed ISBN - 0471135763 Mathematical Economics - Jeffrey Baldani 2nd ed ISBN - 0324183321 Mathematical Ideas - Charles D. Miller 11th ed ISBN - 0321361466 Mathematical Ideas - Charles D. Miller 11th ed ISBN - 0321361482 Mathematical Methods for Economics - Michael Klein 2nd ed ISBN - 0201726262 Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand 2nd ed ISBN - 0321390539 Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand 1st ed ISBN - 0201710900 Mathematical Reasoning for Elementary Teachers - Calvin T. Long 5th ed ISBN - 0321460847 Mathematics for Business - Stanley A. Salzman 8th ed ISBN - 0321357434 Mathematics for Elementary School Teachers - Phares O'Daffer 4th ed ISBN - 0321448049 Mathematics for Physicists - Susan Lea 1st ed ISBN - 0534379974 Mathematics of Interest Rates and Finance - Gary Guthrie 1st ed ISBN - 0130461822 Mathematics with Applications - Margaret L. Lial 9th ed ISBN - 0321334337 Mechanical Behavior of Materials - Norman Dowling 3rd ed ISBN - 0131863126 Mechanics of Materials - James M. Gere 7th ed ISBN - 0534553974 Mechanics of Materials - Russell C. Hibbeler 7th ed ISBN - 0132209918 Medical Imaging Signals and Systems - Jerry L. Prince 1st ed ISBN - 0130653535 Microbiology with Diseases by Body System - Robert W. Bauman 2nd ed ISBN - 032151341X Microbiology: An Introduction - Gerard J. Tortora 9th ed ISBN - 0805347909 Microeconomics - Glenn Hubbard 2nd ed ISBN - 0138132771 Microeconomics - Jeffrey Perloff 4th ed ISBN - 0321414527 Microeconomics - Jeffrey Perloff 5th ed ISBN - 0321531191 Microeconomics - Michael Parkin 7th ed ISBN - 0321454944 Microeconomics - Michael Parkin 8th ed ISBN - 0321416600 Microeconomics - Michael Parkin 9th ed ISBN - 0321600045 Microeconomics - Richard G. Lipsey 13th ed ISBN - 032136922X Microeconomics - Robert Pindyck, Daniel Rubinfeld 6th ed ISBN - 0130084611 Microeconomics - Robert Pindyck, Daniel Rubinfeld 7th ed ISBN - 0132080230 Microeconomics - Roger A. Arnold 9th ed ISBN - 0324785496 Microeconomics: Principles and Policy - William J. Baumol 11th ed ISBN - 0324586221 Microeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin 4th ed ISBN - 0131536060 Microeconomics: Principles, Applications, and Tools - Arthur O'Sullivan 5th ed ISBN - 0131572830 Microeconomics: Public and Private Choice - James D. Gwartney 12th ed ISBN - 0324580207 Microeconomics: Theory and Applications with Calculus - Jeffrey M. Perloff 1st ed ISBN - 0321277945 Microwave Engineering - David Pozar 3rd ed ISBN - 0471448788 MIS Essentials - David Kroenke 1st ed ISBN - 0136075606 MKTG 3.0 2009 Edition - Charles W. Lamb 3rd ed ISBN - 0324789289 Modern Control Systems - Richard C Dorf 11th ed ISBN - 0132270285 Modern Database Management - Jeffrey Hoffer 8th ed ISBN - 0132212110 Modern Database Management - Jeffrey Hoffer 9th ed ISBN - 0136003915 Modern Electronic Communication - Jeff Beasley 9th ed ISBN - 0132251132 Modern Elementary Statistics - John E. Freund 12th ed ISBN - 013187439X Modern Industrial Organization - Dennis Carlton, Jeffrey Perloff 4th ed ISBN - 0321180232 Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg 10th ed ISBN - 0321533739 Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg 9th ed ISBN - 0321305035 Modern Management - Samuel C. Certo 10th ed ISBN - 0131494708 Modern Physics - Randy Harris 2nd ed ISBN - 0805303081 Modern Physics - Raymond Serway 3rd ed ISBN - 0534493394 Modern Semiconductor Devices for Integrated Circuits - Chenming C. Hu 1st ed ISBN - 0136085253 Modern Systems Analysis and Design - Jeffrey A. Hoffer 5th ed ISBN - 0132240769 Modern Wireless Communications - Simon Haykin 1st ed ISBN - 0130224723 Money, Banking and Financial Markets - Roger LeRoy Miller 3rd ed ISBN Money, the Financial System, and the Economy - R. Glenn Hubbard 6th ed ISBN - 0321426703 Multinational Business Finance - David K. Eiteman 11th ed ISBN - 0321357965 Multinational Finance - Kirt C. Butler 3rd ed ISBN - 0324177453 Multinational Management - John B. Cullen 4th ed ISBN - 032442177X Multivariate Data Analysis - Joseph F. Hair 7th ed ISBN - 0138132631 Nanoengineering of Structural, Functional and Smart Materials - Mark J. Schulz 1st ed ISBN - 0849316537 New Venture Management: The Entrepreneur's Roadmap - Donald Kuratko 1st ed ISBN - 0136130321 Numerical Analysis - Timothy Sauer 1st ed ISBN - 0321268989 Numerical Methods for Engineers - Bilal Ayyub, Richard McCuen 1st ed ISBN - 0133373614 Numerical Methods Using Matlab - John Mathews 4th ed ISBN - 0130652482 Occupational Safety and Health for Technologists, Engineers, and Managers - David L. Goetsch 6th ed ISBN - 0132397609 Office Procedures 21st Century & Student Workbook Package - Sharon Burton 7th ed ISBN - 0132343436 OM 2008 - David Alan Collier 1st ed ISBN - 0324662556 Operating Systems Principles - Lubomir F. Bic 1st ed ISBN - 0130266116 Operating Systems: Internals and Design Principles - William Stallings 5th ed ISBN - 0131479547 Operations Management - Jay Heizer 8th ed ISBN - 0131554441 Operations Management - Jay Heizer 9th ed ISBN - 0138128782 Operations Management - Nigel Slack 5th ed ISBN - 0273708473 Operations Management and Student CD and Student DVD Package - Jay Heizer 9th ed ISBN - 0138128782 Operations Management: Process and Value Chains - Lee J. Krajewski 8th ed ISBN - 0131697390 Operations Research: An Introduction - Hamdy A. Taha 8th ed ISBN - 0131889230 Opportunities and Challenges of Workplace Diversity: Theory, Cases, and Exercises - Kathryn Canas 1st ed ISBN - 0131343068 Oracle 10g Programming: A Primer - Rajshekhar Sunderraman 1st ed ISBN - 0321463048 Organic Chemistry - Paula Bruice Test Bank only 5th ed ISBN - 0131963163 Organization Development and Change - Thomas G. 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Clarkson 10th ed ISBN - 0324303904 Wireless Communications & Networks - William Stallings 2nd ed ISBN - 0131918354 Writing and Speaking at Work: A Practical Guide for Business Communication - Edward P. Bailey 4th ed ISBN - 0131881302 Your Attitude is Showing - Sharon Lund O'Neil 12th ed ISBN - 0132429047 === Subject: graphs and minimum spanning trees Let T be a minimum spanning tree (MST) for the graph G. Let e(u,v) be an edge of G not in T. Let's suppose we decrease the weight of e(u,v) and we want to find the new MST. We proceed as follows: 1) We add e(u,v) to T. By doing so we are bound to create a loop. 2) We remove the lightest edge from that loop. How can we prove that this algorithm actually works? I found the algorithm and I suspect it works, but I can't prove it! Kiuhnm === Subject: Re: graphs and minimum spanning trees > Let T be a minimum spanning tree (MST) for the graph G. > Let e(u,v) be an edge of G not in T. > Let's suppose we decrease the weight of e(u,v) and we want to find the > new MST. We proceed as follows: > 1) We add e(u,v) to T. By doing so we are bound to create a loop. > 2) We remove the lightest edge from that loop. How can we prove that this algorithm actually works? > I found the algorithm and I suspect it works, but I can't prove it! Find a description of Kruskal's algorithm, together with a proof of its correctness (most textbooks with discrete mathematics in the title will have this). Then think about how you can modify the proof to meet your situation. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: quasi-isomorphisms for DGA Let A and B are DG algebras over field k. Is it right that A quasi-isomorphic to B as DG-algebra iff there is A_{infinity}-quasi-isomorphism between them? === Subject: Re: Solutions manual to Engineering and Chemical Thermodynamics by Milo D. Kore posting-account=V7kruQoAAAAPPE8oGX1CC6Omgf6Q9BMf 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) New Solution Manuals Email at servicepp(at)hotmail.com (please replace (at) with @), if the solution you want is not on the list, email at me. Instructor Solutions manual to: Edition ,By F. P. Beer, E. R. Johnston 2 Modern Control Systems 11th by Richard C Dorf and Robert H. 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Kraige 14 Solution manual to Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER 15 Solution manual to Engineering Mechanics - Statics (11th ) by R.C.HIBBELER 16 Solutions manual to Separation Process Principles, 2nd Ed, by Seader, Henley 17 Solutions manual to Numerical methods for engineers 5th by Chapra 18 Solutions manual to Elements of engineering electromagnetic (6/e) by N.N.RAO 19 Solution manual to Financial Accounting 6e by horngren Harrison 20 Solution manual to Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik 21 Solution manual to Complex Variables with Applications (Pie) by A.David Wunsch 22 Solution manual to Computer Design Fundamentals4E by Mano and Kime. 4th 23 Solution manual to Computer Networks Systems Approach 3ed by davie peterson 24 Solution manual to COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING 25 Solution manual to Cost Accounting, 13/e 13e by Horngren 26 Solution manual to Data and Computer Communications, 7th Edition By Stallings 27 Solution manual to Differential Equations and Linear Algebra by Penney and Edwards, 2nd edition 28 Solution manual to Elementary Differential Equations and Boundary Value Problems, by Boyce andDiprima 29 Solution manual to Elements of engineering electromagnetics (6/ e) by N.N.RAO 30 Solution manual to Financial Accounting 6e by horngren Harrison 31 Solution manual to Financial management theory and practice 12e by Brigham 32 Solution manual to Fundamentals of Applied Electromagnetics 5th edition by Fawwaz T. 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Jaeger 3rd edition 41 Solution manual to Numerical methods for engineers 5th by Chapra 42 Solution manual to Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole 43 Solution manual to Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis 44 Solution manual to Separation Process Principles, 2nd Ed., by Seader, Henley 45 Solution manual to Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition 46 Solution manual to Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith Edition By F. P. Beer, E. R. Johnston 48 Solution manual to Young & Freedman University Physics, 12th Edition 49 solution manual for Probability and Statistical Inference ( 7th edition by Hogg & Tanis) 50 solution manual to Fundamentals of Physics (8th_Edition) By Halliday 50 solution manual to Engineering and Chemical Thermodynamics by Wyatt Tenhaeff Milo Koretsky Solutions manua to Corporate Finance 1e by Berk SM Solutions manual to Introduction to Environmental engineering and science 3rd editions by Gilbert M. Masters Solutions manual to Introduction to Mathematical Statistics 6/E Robert V. Hogg Solutions manual to Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Solutions manual to Intermediate Miroeconomics: Homawork and solutions (Varian Solutions manual to Econometric Analysis(Greene 6e, 2008) Solutions manual to computer system architecture 3rd by M.Morris Mano Solutions manual to Design Analysis in Rock Mechanics By William G. Pariseau Solutions manual to Digital Design 4th by M. Morris Mano, Michael D. Ciletti Solutions manual to Engineering and Chemical Thermodynamics by Milo D. Koretsky Solutions manual to Fundamentals of Clas Sical Thermodynamics 6th edition by Van Wylen Solutions manual to Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Solutions manual to Mechanical Vibrations, Third Edition, by Singiresu S. Rao Solutions manual to Microelectronic Circuit Analysis and Design, 3ed. by Neamen (2006) - [Solutions Manual Only] by Donald A. Neamen Solutions manual to Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Solutions manual to Modern Organic Synthesis: An Introduction by Michael H. Nantz, Hasan Palandoken, George S. Zweifel Solutions manual to Power System Analysis By John J. Grainger, William D. Stevenson Jr Solutions manual to Investments Student Solutions Manual 6e by Zvi Bodie Solutions manual to Auditing and Assurance Services 12 th by: Alvin A Arens, Randal J Elder, Mark Beasley Solutions manual to Signals and Systems: Analysis of Signals Through Linear Systems by: M.J. Roberts, M.J. Roberts === Subject: Reactions to/against the Binary Tree posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) During the last years the complete infinite binary tree and its implications on set theory have been on topic frequently. Here is the collection of counterarguments that have come to my attention. If you think there is another counter-argument (or pro-argument), or if you think to have an argument that improves one of the presented arguments, please feel free to append it. I would be glad however, if only serious contributions were added and if all unqualified comments and statements of pure opinions could be suppressed. Theorem: The complete infinite binary tree has only countably many infinite paths. 0. / 0 1 / / 0 10 1 ... Proof A) Construct the binary tree starting from a tree that has only one path, say p 0 = 0.000... 0. | 0 | 0 | 0 ... Add all paths that end by infinitely many zeros. Every path that you add must start at a node of p 0 or at a node of a path already constructed. The number of paths in the tree grows by not more and not less than 1 when 1 path is added. However, after completing that procedure all nodes and every infinite sequence of bits (including the path 0.111...) is represented in the infinite binary tree. Proof B) The complete infinite binary tree can be constructed by an infinite agglomeration of basic elements of the form | o / The number of distinct lines is increased by 1 by 1 node. lines going out - lines coming in - nodes = 2 - 1 - 1 = 0 . This procedure, even when applied infinitely often, cannot but yield the result 0 implying a countable number of lines. The set of all lines limits the set of all distinct paths. The construction is possible in (B) as well as in (A) because the numbers of elements used for construction is countably infinite. Proof C) Consider the edges of the complete binary tree (an edge connects two subsequent nodes of a path). Take all edges and put them on one and the same level of the tree, side by side, such that the tree now is an array of parallel edges: |||||||... This array limits the number of possible paths of the tree. It is an upper limit, because every path there has only one edge. And there is no further edge remaining to distinguish any further paths. Remark: Of course a set of n edges can be put in n! different sequences. But the edges of the binary tree are not subject to arbitrary ordering. Each one has one and only one fixed place in the tree. Therefore the number of edges limits the number of paths. Proof C gives an upper limit. Remark: The tree contains all possible sequences of bits including 0.111... . Nevertheless the tree contains only a countable number of paths, as we see by each of the arguments (A, B, and C). This shows that most of the real numbers cannot exist as independent bit sequences. It shows further that most of the real numbers are not subject to being put in a list or resulting from a list as an anti-diagonal number. For visualising the construction of the binary tree see: http://www.hs-augsburg.de/~mueckenh/GU/GU12.PPT#335,24,Folie 24 Vaughan Pratt: http://www.cs.nyu.edu/pipermail/fom/2009-March/013493.html In the finite case, each node at depth d from the root of a tree of height h participates in 2^(h-d) paths. As h increases that node participates in an exponentially growing number of paths. Therefore in the limit each node participates in 2^N paths. Now you might say, oh, but there are twice as many new nodes at every height increment. So then we have to ask whether this is enough node growth at depth h to offset the exponentially growing number of paths shared by one node at depth d. In the limit each path is shared between N nodes, but that still leaves 2^N/N paths per node, which cannot be N because N^2 is countable and 2^N is not. My comment: It is just under investigation whether 2^N is larger than the number of nodes which, by the way, is 2^N, if the tree has N levels. Vaughan Pratt: http://www.cs.nyu.edu/pipermail/fom/2009-March/013493.html Since the infinite case does not count the leaves (there being none), it would be misleading to count them in the finite case if we want insight into what happens at infinity. For trees of height h we find a cardinality gap: 2^h - 1 interior nodes vs. 2^h paths. Why should passing to the limit close this gap? My answer: A good argument. Let us start with a pre-root node o | o / Then there is no gap from the beginning. Why should passing to the limit open a gap? Vaughan Pratt: http://www.cs.nyu.edu/pipermail/fom/2009-March/013493.html Every pair of nodes is connected by a finite path, whereas every pair of paths has in common only finitely many nodes and they differ by infinitely many nodes. Therefore any comparison of nodes to paths is an apples-to-oranges comparison for which it would very surprising to find a bijection between them. My answer: There is no bijection, but as proof A shows, there are not more paths than nodes. David C. Ullrich (alluding to proof B): You say This procedure, even when applied infinitely often, cannot but yield the result 0 respectively a countable number of lines. over and over, but it's simply not true. Your asserting it does not make it true. The fact that it seems clearly true to you does not make it true. You need to give a proof of this, and you've never done so - in each of your attempts there's always a similar unjustified assertion. My answer: For the infinite sum over all (countably many) basic elements it should be clear that SUM[n --> oo] 2 - 1 - 1 = SUM[n --> oo] 0 = 0. Without proof. But even if we had only SUM[n --> oo] 2 - 1 - 1 = SUM[n --> oo] 0 < 2^aleph 0 there would be less than 2^aleph 0 paths. Proof of the latter: SUM[n --> oo] 0 =< SUM[n --> oo] 1 = oo < 2^aleph 0 (if the disproved result were correct.) Owen Jacobson: Every infinitely-long binary string constructed this way has only finitely many 1s. There infinitely-long binary strings which contain more than finitely many 1s, but your construction will not create them at any step, so you cannot inductively prove things from the properties of the strings your construction creates to strings that your construction omits. More surprising, though, is the fact that your construction demonstrably constructs at least one path through every node in the tree! For any node, we can construct an initial path leading to it using a finite number of 1s and 0s, and we can then proceed using finitely many more 1s to any of its descendent nodes, but at some point on each path, your construction gives up and generates infinitely many zeros. My answer: I don't give up before Cantor gives up in his diagonal argument. Construction according to A or B supplies the complete set of paths. Virgil All those with infinitely many 1's in them [are missing] My answer: I cannot find any missing path. Construction according to A or B supplies the complete set of paths. Calvin Ostrum: Here, I think, is your problem. You are not noticing that when you add a single path, you are actually adding many paths. My answer: According to construction A this is false. Calvin Ostrum : The net result in the end is that after all your paths have been added, there are many other paths that exist, because of the edges that have been added to make the paths, which you have not noticed. My answer: According to construction A this is false. Calvin Ostrum: Every path you add is of the form a finite sequence of 0's and 1's, following by infinite sequence of 0's. However, there are paths in the final tree that are not like this. That is because the paths interact with one another. You must look at the individual edges and how then can be made into paths in the final tree. You do not add paths, you add edges. Paths come FOR FREE. You cannot pick and choose the paths you add. They sneak in as sets of joined edges and there is nothing you can do about it. My answer: I cannot believe that an uncountable set of different paths can be individually constructed by a countable number of steps. Christopher Creutzig: My translation (of the German original, cp. also for some other arguments, related to some already discussed above): A path is not defined by a single node but by an infinite number of them. Therefore the number of nodes is not an upper limit for the number of paths, at least not automatically. My answer: Every path can be distinguished by one single node from every selected set of paths. Of course first the selected set must be defined by individually picking the paths belonging to that set, as is usual in logic. If infinitely many nodes were needed to define a single path, then you should be able to present at least one of the set of needed nodes. Christopher Creutzig: All attempts to construct an explicit surjection of the set of nodes onto the set of paths have been contradicted by the explicit presentation of paths that are not in this surjection. My answer: I do not present a surjection. Only countably many paths can be counted. But in order to construct the whole tree countably many paths are sufficient. Further, according to proof A, the number of nodes occupied by constructed paths grows by aleph 0 with every single path appended. Georg Cantor Letter to Vivanti of Dec. 3 1885 Cantor discusses what now is known as the construction of the binary tree. Consider all finite paths: z n = (a 1)/2 + (a 2)/2^2 + ... + (a (n-1))/2^(n-1) + 1/2^n with a k having value 0 oder 1. The number of them is z n is 2^ (n-1). For n = 1, 2, 3, ... in inf. then 1+ 2 + 4 + 8 + ... in inf. z == {z 1, z 2, z 3, ...} But these numbers are merely a very small subset of all numbers that have the form z n = (a 1)/2 + (a 2)/2^2 + ... + (a n)/2^n + ... in inf. and make up a set of second cardinality (the infinite paths). This apparent difficulty is solved as follows: The set of all numbers of the unit interval is not the limit of all finite path z n for n = oo. My answer: If the set of real numbers of the unit interval (infinite paths) cannot be considered as the limit of the set of finite paths, why then should any irrational number be considered as the limit of the sequence of its finite initial segments (i.e., as an infinite path in the binary tree)? This would be extremely inconsequent. The question would arise: How many real numbers can be considered as the limits of the sequences of their finite initial segments? Only one at a time, or two or ten or aleph 0 or some number depending on the brain capacity of the observer? But if consequently denying the limit process, then also 0.111... is not the limit of 0,1 0,11 0,111 ... Then Cantor's diagonal argument fails, because then there is not a diagonal number 0.111... that is different from all its finite initial segments. Then also Cantor's construction of irrational numbers fails, as given by himself in [Bemerkungen mit Bezug auf den Aufsatz: Zur Weierstra¤-Cantorschen Theorie der Irrationalzahlen (Werke p. 114)] : sqrt(3) = (1,7, 1,73, 1,732, ...) === Subject: Re: Reactions to/against the Binary Tree Content-ID: <20090524233927.K94629@agora.rdrop.com Theorem: The complete infinite binary tree has only countably many > infinite paths. 0. > / > 0 1 > / / > 0 10 1 > ... You are trying to prove the impossible as the conjectured theorem is false. If you want to prove the reals are countable, then consider the Skolem paradox that shows that if ZF is consistent, then it has a countable model. === Subject: Re: Reactions to/against the Binary Tree <20090524231849.H94629@agora.rdrop.com> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Theorem: The complete infinite binary tree has only countably many > infinite paths. > 0. > / > 0 1 > / / > 0 10 1 > ... You are trying to prove the impossible as the conjectured theorem is false. If so, then we have to tolerate the follwing situation: The real number sqrt(3) is the limit of a rational sequence. Every real number is the imit of a rational sequence. Not every number is the limit of a rational sequence. Because not all real numbers are the limits of rational sequences. I do not tolerate that situation. If you want to prove the reals are countable, then consider the Skolem > paradox that shows that if ZF is consistent, then it has a countable > model. Skolem said: Erstens habe ich eine genauere Begr.9fndung des allgemeinen mengentheoretischen Relativismus gegeben, der besonders die Konsequenz hat, da¤ das Absolut-nicht-abz.8ahlbare auf axiomatischer Grundlage keine Existenzberechtigung hat. ... The absolute meaning of uncountable is not justified on an axiomatic basis. === Subject: Re: Reactions to/against the Binary Tree posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > During the last years the complete infinite binary tree and its > implications on set theory have been on topic frequently. Here is the > collection of counterarguments that have come to my attention. If you think there is another counter-argument (or pro-argument), or > if you think to have an argument that improves one of the presented > arguments, please feel free to append it. I would be glad however, if > only serious contributions were added and if all unqualified comments > and statements of pure opinions could be suppressed. A simple counter-argument (I suppose this might be an informal version of your proof A): [tree height] < [num. of paths] < [num. of nodes] 0 < 0 < 0 1 < 2 < 2 2 < 4 < 6 3 < 8 < 14 4 < 16 < 30 ... n < 2^n < 2^(n+1)-2 (for n > 0) ... Extending to the infinite case (here the notation might need fixing and I'm not sure if the inequalities should still be strict, but this is irrelevant to the conclusion): w <= 2^w <= 2^(w+1)-2 Since the number of nodes is countable, i.e.: |w| = |2^(w+1)-2| Follows: |w| = |2^w| = |2^(w+1)-2| IOW, that is: The number of nodes is countable; The number of paths is dominated by the number of nodes; Therefore: The number of paths is countable. -LV === Subject: Re: Reactions to/against the Binary Tree > During the last years the complete infinite binary tree and its > implications on set theory have been on topic frequently. Here is the > collection of counterarguments that have come to my attention. > If you think there is another counter-argument (or pro-argument), or > if you think to have an argument that improves one of the presented > arguments, please feel free to append it. I would be glad however, if > only serious contributions were added and if all unqualified comments > and statements of pure opinions could be suppressed. A simple counter-argument (I suppose this might be an informal version > of your proof A): [tree height] < [num. of paths] < [num. of nodes] 0 < 0 < 0 > 1 < 2 < 2 > 2 < 4 < 6 > 3 < 8 < 14 > 4 < 16 < 30 > ... > n < 2^n < 2^(n+1)-2 (for n > 0) > ... Extending to the infinite case (here the notation might need fixing > and I'm not sure if the inequalities should still be strict, but this > is irrelevant to the conclusion): So it is. w <= 2^w <= 2^(w+1)-2 Since the number of nodes is countable, i.e.: |w| = |2^(w+1)-2| Follows: |w| = |2^w| = |2^(w+1)-2| IOW, that is: The number of nodes is countable; > The number of paths is dominated by the number of nodes; > Therefore: > The number of paths is countable. > I agree. There is another argument. For every appended path we inrease the number of nodes by aleph 0, the number of paths by 1. This should suddenly switch when finishing the infinite? Ad if it cannot be finished, then the whole discussion about cardinalities is in vain. === Subject: Re: Reactions to/against the Binary Tree posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) Extending to the infinite case You can't just blithely extend to the infinite case. Infinite is not just a bigger kind of natural number. Marshall === Subject: Re: Reactions to/against the Binary Tree If you think there is another counter-argument (or pro-argument), or > if you think to have an argument that improves one of the presented > arguments, please feel free to append it. I would be glad however, if > only serious contributions were added and if all unqualified comments > and statements of pure opinions could be suppressed. This is not an argument either pro- or anti-, but it is a serious comment nevertheless. You have put enormous effort into tearing down parts of existing mathematics. You find fault with set theory, with the real numbers, the existence of very large natural numbers, etc. Leaving entirely aside what I think of your arguments, I notice that you never advance any theory of your own. You have never provided anything constructive. Always with you it is trying to destroy, never to create. Don't you think your time would be better spent, don't you think your arguments would be more persuasive, if you provided an actual alternative? I think you should put your time into formalizing your ideas. As it stands, and again even without any judgment of your arguments, you are no pioneer, merely a naysayer. Marshall === Subject: Re: Reactions to/against the Binary Tree posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > If you think there is another counter-argument (or pro-argument), or > if you think to have an argument that improves one of the presented > arguments, please feel free to append it. I would be glad however, if > only serious contributions were added and if all unqualified comments > and statements of pure opinions could be suppressed. This is not an argument either pro- or anti-, but it is a serious > comment nevertheless. I see and appreciate that. Therefore I answer. You have put enormous effort into tearing down parts of existing > mathematics. You find fault with set theory, with the real numbers, Both are unresolvably connected. An entangled state. Cantor knew it. > the existence of very large natural numbers, etc. I do not deny the existence of very large numbers, but only the existence of numbers that require more information for identification (or definition) than is available. Leaving entirely aside what I think of your arguments, That's deplorable. I think that in particular Cantor's text and my answer shows the problem in clearest possible way. > I notice > that you never advance any theory of your own. You have never > provided anything constructive. Always with you it is trying > to destroy, never to create. Recently I have written a text book on elementary mathematics. I did not find anything to change with current mathematics. The reason is that set theory has not really influenced mathematics. So I simply explained in the preface that there are no actual infinities --- and everything runs its way. What should I change? *That* mathematics does not allow quantifier exchange. http://www.oldenbourg-wissenschaftsverlag.de/olb/de/1.c.1598342.de?hasjs=124 3187687&submittedByForm=1&_lang=de&gsid=1.c.325875.de&id=1598342 Don't you think your time would be better spent, don't you think > your arguments would be more persuasive, if you provided an > actual alternative? I think you should put your time into formalizing your ideas. I agree with Doron Zeilberger: The Human Obsession With Formal Proofs is a Waste of the Computer's Time, and, Even More Regretfully, of Humans' Time. (Opinion 94) Formalization has not protected many extremely intelligent minds from set theory. > As it stands, and again even without any judgment of your > arguments, you are no pioneer, merely a naysayer. Without us evolution would sometimes run out of control === Subject: Re: Reactions to/against the Binary Tree posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > You have put enormous effort into tearing down parts of existing > mathematics. You find fault with set theory, with the real numbers, Both are unresolvably connected. An entangled state. Cantor knew it. I agree. > the existence of very large natural numbers, etc. I do not deny the existence of very large numbers, but only the > existence of numbers that require more information for identification > (or definition) than is available. Yes; that is what I should have said. Sometimes this excessive information requirement results in a very large number, but in other cases it could be between 0 and 1. > Leaving entirely aside what I think of your arguments, That's deplorable. I think that in particular Cantor's text and my > answer shows the problem in clearest possible way. Well, I would hope to be able to address one issue at a time, rather than be required to discuss everything all at once. Would it work for you if I said Leaving aside *temporarily* what I think of your arguments ... > I notice > that you never advance any theory of your own. You have never > provided anything constructive. Always with you it is trying > to destroy, never to create. Recently I have written a text book on elementary mathematics. I did > not find anything to change with current mathematics. The reason is > that set theory has not really influenced mathematics. So I simply > explained in the preface that there are no actual infinities --- and > everything runs its way. What should I change? My immediate reaction is, if nothing changes, then why is it such an issue for you? Why bother arguing over a difference that makes no difference? It seems pointless. > *That* mathematics does not allow quantifier exchange. http://www.oldenbourg-wissenschaftsverlag.de/olb/de/1.c.1598342.de?ha... My congratulations to you on the occasion of the publishing of your book. > Don't you think your time would be better spent, don't you think > your arguments would be more persuasive, if you provided an > actual alternative? > I think you should put your time into formalizing your ideas. I agree with Doron Zeilberger: The Human Obsession With Formal > Proofs is a Waste of the Computer's Time, and, Even More Regretfully, > of Humans' Time. (Opinion 94) I disagree. Machine-checked anything is useful because machines are so much more fastidious than humans. It is true that machine checked proof is no defense against garbage in, garbage out but it is certainly an excellent defense against mistaken deduction, and that is something all humans are subject to. I also have my example of the affirmative conclusion to the Robbins Conjecture, which was pursued manually by humans for decades to no avail, but was solved instead by the EQN software. This software was itself written by humans of course. Also: mechanical proof software is fun. (Perhaps not universally, though; I suppose I could *imagine* someone somewhere might not find it as interesting as I do. My wife, say.) > Formalization has not protected many extremely intelligent minds from > set theory. > As it stands, and again even without any judgment of your > arguments, you are no pioneer, merely a naysayer. Without us evolution would sometimes run out of control I am curious, can you name any event in math history that would be an example of a success of the type you seek: finding fault with established theory? This is not a rhetorical question; I have some modest interest in math history, and I can't think of an example. But if there is one, I'd be interested to hear of it. Marshall === Subject: Re: Reactions to/against the Binary Tree posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Martin Musatov > May I ask what is your opinion with respect to the binary tree? === Subject: Re: Reactions to/against the Binary Tree May I ask what is your opinion with respect to the binary tree? That guy is just a prankster. His only interest is to wind people up. Marshall === Subject: Re: Reactions to/against the Binary Tree > May I ask what is your opinion with respect to the binary tree? That guy is just a prankster. His only interest is to wind > people up. > In this case my interest was the same. === Subject: Re: Reactions to/against the Binary Tree > Martin Musatov > May I ask what is your opinion with respect to the binary tree? That guy is just a prankster. His only interest is to wind > people up. Probably. And what does it tell about Mueckenheim that he didn't notice that but asked the question above? Ralf === Subject: Re: Reactions to/against the Binary Tree posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Yes; that is what I should have said. Sometimes this excessive > information requirement results in a very large number, but in > other cases it could be between 0 and 1. So it is. Pi is defined by many finite formulas. But if a finite formula is lacking, as unavoidably must be the case for most reals, then it is impossible to define or to use them as individuals. The decimal expansion of pi or even that of 1/33 = 0.030303... does not exist _in the real world_, because not all natural numbers required as indices (counting the places) are available, be it in written, thought or what ever form. > Leaving entirely aside what I think of your arguments, > That's deplorable. I think that in particular Cantor's text and my > answer shows the problem in clearest possible way. Well, I would hope to be able to address one issue at a > time, rather than be required to discuss everything all at > once. Would it work for you if I said Leaving aside > *temporarily* what I think of your arguments ... > I notice > that you never advance any theory of your own. You have never > provided anything constructive. Always with you it is trying > to destroy, never to create. > Recently I have written a text book on elementary mathematics. I did > not find anything to change with current mathematics. The reason is > that set theory has not really influenced mathematics. So I simply > explained in the preface that there are no actual infinities --- and > everything runs its way. What should I change? My immediate reaction is, if nothing changes, then why > is it such an issue for you? Why bother arguing over a > difference that makes no difference? It seems pointless. There are two reasons: First set theorists have conquered mathematics claming that only mathematics based upon set theory (and only in formalized form) is real mathematics. Everything else is unclear prose. I do not believe that. I am sure that later times will find that automatized proofs are not automatically true. Second, there are some scholars who try to prove theorems about finite numbers by means of infinite cardinals. Such attempts are in vain. But in fact, I see that finished infinity is such a hocus pocus that I cannot be silent. I also have my example of the affirmative conclusion to the > Robbins Conjecture, which was pursued manually by humans > for decades to no avail, but was solved instead by the EQN > software. This software was itself written by humans of course. That is another issue. Of course a machine may be used to find a solution of an involved or difficult combinatorical problem. I use calculators and Mathematica for many purposes. But I do not believe, like some, that a proof of Cantor's theorem, once checked by a machine, establishes absolute truth. The machine uses some basics that can be false. > I am curious, can you name any event in math history that > would be an example of a success of the type you seek: > finding fault with established theory? This is not a rhetorical > question; I have some modest interest in math history, and > I can't think of an example. But if there is one, I'd be interested > to hear of it. Naysayer Hippasos von Metapont showed that the pythagorean theorem everything is number (or ratio) was wrong (without introducing irrational numbers, he left that to Eudoxos). Naysayer Nicole d'Oresme denied established knowledge, then the Bible, and proposed the heliocentric system, contradicting the Bible. (Fortunately for him, nobody cared at that time.) In 1833 Legendre presented to the French academy six proofs of the parallel axiom, three of them working with infinite angular areas. Naysayer Gauss did not dare to publish his results concerning geometry. The other way round: Christian Doppler stated his theory by 1850. Though being extremely simple, it was rejected by all great Austrian (and other) mathematicians for more than 30 years. As late as in 1900 a physics handbook appeared, saying that Doppler's theory is probably correct. === Subject: Integrators of RS integral posting-account=JVPKNAoAAADT8GA9RydVIuuyOWRYhdVD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) Given alpha in the space of functions of bounded variation on [a, b], denoted BV[a, b], is there a function beta in BV[a, b], with beta (a) = 0 such that beta is right-continuous on (a, b) and the Integral from a to b of f d alpha = Integral from a to b of f d beta for all f in C [a, b]? What if alpha is left-continuous but not right-continuous, such as the least integer function? Can such a beta be found? 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Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 113. Vector Mechanics for Engineers: statics, 8th Edition .81iSOLUTIONS MANUAL.81j === Subject: Find a counter-example for linear transformation We know that a linear transformation has the following properties: 1.T(x+y)=T(x)+T(y) 2.T(cx)=cT(x) may there be a mapping T which is true for 1 but false for 2? === Subject: Re: Find a counter-example for linear transformation > We know that a linear transformation has the following properties: > 1.T(x+y)=T(x)+T(y) > 2.T(cx)=cT(x) No, we don't _know_ that. We _define_ linear transformation as a map with these properties. > may there be a mapping T which is true for 1 but false for 2? That depends upon the field that you are working with. If it's the field of rational numbers, then the answer is negative. If you you are working with the complex field, then the answer is positive: just take the conjugation from C into itself. Over the reals the answer is also positive, but harder to prove; it requires the axiom of choice. See http://mathworld.wolfram.com/CauchyFunctionalEquation.html for instance. Jose Carlos Santos === Subject: Re: Find a counter-example for linear transformation > We know that a linear transformation has the following properties: > 1.T(x+y)=T(x)+T(y) > 2.T(cx)=cT(x) may there be a mapping T which is true for 1 but false for 2? Kiuhnm === Subject: Re: Find a counter-example for linear transformation > We know that a linear transformation has the following properties: > 1.T(x+y)=T(x)+T(y) > 2.T(cx)=cT(x) may there be a mapping T which is true for 1 but false for 2? Consider a vector space V(N,+,*,R), where the vectors are the natural numbers and the field is R, the set of the real numbers. Kiuhnm === Subject: Re: Find a counter-example for linear transformation > We know that a linear transformation has the following properties: > 1.T(x+y)=T(x)+T(y) > 2.T(cx)=cT(x) > may there be a mapping T which is true for 1 but false for 2? Consider a vector space V(N,+,*,R), where the vectors are the natural > numbers and the field is R, the set of the real numbers. Ehm...V(N,+,*,R) is not a vector space. In my example T(1/2 x) is undefined so point 2 is not true. Kiuhnm === Subject: Re: Hi ! Long time no see ! (Set problem) > A = {2, 5} > B = {2, 3, a, a+3} > A subset B > Find all a. (a : postive integer) > (1) a = 5 > (2) a = 2 or 5 > ------------------------------------------------------------------------ > What's your answer among (1) , (2) ? Bonjour Mina, nice to meet you again, > my answer (1) a =5 ,no repetition allowed, Bonjour Alain, what's wrong with a=2? Isn't B = {2,3,5} if you let a=2? So this a=2 is a wonderful value a, yielding A subset B. Your no repetition allowed is out of place. You may write B = {2,3,2,2+3}, but this is as correct as B={5,2,3} or B={p|p<6 and p prime} or B={5-3,-(2-5),7-2} as all these notations describe the same set. Rainer === Subject: Re: Hi ! Long time no see ! (Set problem) >Hello teacher~ I teach in a middle school. >Teacher is really busy. A = {2, 5} >B = {2, 3, a, a+3} A subset B Find all a. (a : postive integer) (1) a = 5 >(2) a = 2 or 5 ------------------------------------------------------------------------ >What's your answer among (1) , (2) ? > iT saya all a -- that's 2 and 5 === Subject: Re: Hi ! Long time no see ! (Set problem) > I teach in a middle school. > Teacher is really busy. A = {2, 5} > B = {2, 3, a, a+3} A subset B Find all a. (a : postive integer) > No no, multiple choice. Let's have real problem. Find all a for which A subset B. Show your work. A subset B iff 2 in B, 5 in B iff 5 in B iff a = 5 or a + 3 = 5 === Subject: Turing machine as solution of PDE posting-account=AphEFQoAAADpN_uxZavuHwV48pQ6OAwv Gecko/2009042708 Fedora/3.0.10-1.fc10 Firefox/3.0.10,gzip(gfe),gzip(gfe) It is well known and quite obvious, that Turing machine can be implemented inside a cellular automation of some kind. There are lots of such constructs, both for 1D cellular automatons and 2D (including the Game of Life). But cellular automatons are discrete, both in time and space. I am curious: are there any partial differential equations, which can be used for constructing the Turing machine? Well, I am quite sure that there are a lot of such PDEs. The real question is, what they are. For example, the sine-gordon equation seems to have dynamic, complex enough for hosting such construct. me. === Subject: Re: Turing machine as solution of PDE posting-account=5t-ZfgkAAACU7ydoC4Cq-xVNAFsq481f Gecko/2009050804 Mandriva/1.9.0.10-0.1mdv2009.1 (2009.1) Firefox/3.0.10,gzip(gfe),gzip(gfe) > It is well known and quite obvious, that Turing machine can be > implemented inside a cellular automation of some kind. There are lots > of such constructs, both for 1D cellular automatons and 2D (including > the Game of Life). But cellular automatons are discrete, both in time > and space. I am curious: are there any partial differential equations, which can > be used for constructing the Turing machine? Well, I am quite sure > that there are a lot of such PDEs. The real question is, what they > are. For example, the sine-gordon equation seems to have dynamic, > complex enough for hosting such construct. In Bible it is called spirit (used the same word as for wind). I'm not sure whether it takes ionosphere magnetic field into account when calculating winds or just simple movement of air. > me. Search for spirits? :-) === Subject: Re: If Cantor set is uncountable and measure 0, then (Cantor)^c has measure 1 on [0, 1]? >I'm trying to get this straight. The Cantor set is uncountable and has >no interior; it's a collection of points. So the complement of the >Cantor set is a collection of open sets. Is the total set of points in >the open sets uncountable? It must be, it seems to me, since any open >set of real numbers contains uncountably many points. And the >complement of the Cantor set on [0, 1] has to have measure 1, no? So >both the Cantor set and its complement are uncountable? It would seem >a paradox if the complement of the Cantor set on [0, 1] were >countable. Why is this a paradox? Both halves of the unit interval are uncountable. >Another question: I've seen it claimed that the Cantor set can be >modified so as to have measure 1 (on [0, 1], for example). Can someone >provide an example of a modified Cantor set with measure 1 on [0, 1]? Not measure 1, but arbitrarily close. At the k-th stage, remove the middle epsilon_k from what is left. Then the measure of the resulting set, which is homeomorphic to the usual Cantor set, is the product of (1 - epsilon_k). -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: If Cantor set is uncountable and measure 0, then (Cantor)^c has measure 1 on [0, 1]? posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I'm trying to get this straight. The Cantor set is uncountable and has > no interior; > Yes. > it's a collection of points. > Yes, but that's a strange comment. > So the complement of the > Cantor set is a collection of open sets. > I think you meant to say the complement of the Cantor set is open. He may have meant either and still been correct. If he would have said that the cantor set is the union of the collection. > Is the total set of points in > the open sets uncountable? It must be, it seems to me, since any open > set of real numbers contains uncountably many points. And the > complement of the Cantor set on [0, 1] has to have measure 1, no? So > both the Cantor set and its complement are uncountable? It would seem > a paradox if the complement of the Cantor set on [0, 1] were > countable. > Another question: I've seen it claimed that the Cantor set can be > modified so as to have measure 1 (on [0, 1], for example). Can someone > provide an example of a modified Cantor set with measure 1 on [0, 1]? > There are Cantor sets that have measure 1, but they are not a subset > of [0,1]. Cantor sets are compact, and a compact subset of [0, 1] of > measure 1 must be [0, 1] itself. > -- > Virgil === Subject: Re: If Cantor set is uncountable and measure 0, then (Cantor)^c has measure 1 on [0, 1]? posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I'm trying to get this straight. The Cantor set is uncountable and has > no interior; > Yes. > it's a collection of points. > Yes, but that's a strange comment. > So the complement of the > Cantor set is a collection of open sets. > I think you meant to say the complement of the Cantor set is open. > He may have meant either and still been correct. If he would have said that the cantor set is the union of the > collection. the cantor set --> the complement of the cantor set > Is the total set of points in > the open sets uncountable? It must be, it seems to me, since any open > set of real numbers contains uncountably many points. And the > complement of the Cantor set on [0, 1] has to have measure 1, no? So > both the Cantor set and its complement are uncountable? It would seem > a paradox if the complement of the Cantor set on [0, 1] were > countable. > Another question: I've seen it claimed that the Cantor set can be > modified so as to have measure 1 (on [0, 1], for example). Can someone > provide an example of a modified Cantor set with measure 1 on [0, 1]? > There are Cantor sets that have measure 1, but they are not a subset > of [0,1]. Cantor sets are compact, and a compact subset of [0, 1] of > measure 1 must be [0, 1] itself. === Subject: Re: Wikipedia Math > On May 24, 1:43?am, Jon Solution to the Quadradic: > http://en.wikipedia.org/wiki/Quadratic_equation > Solution to the Cubic: > http://en.wikipedia.org/wiki/Cubic_equation > Solution to the Quartic: > http://en.wikipedia.org/wiki/Quartic_function > Solution to the Quintic > http://en.wikipedia.org/wiki/Quintic_equation > there is no formula for general quintic equations > over the rationals in terms of radicals > Defying quantum entanglement was a stroke of genius > in Musatov's proof > P=NP. > See: > thread/ec7e95813d6886f2/f1469447927935b1?lnk=raot#f146 > 9447927935b1 In what way is that related to the original post? === Subject: Re: f(x) + 2x = f(f(x)) > William Elliot a ?crit : > Are there any solutions, R into R, for > f(x) + 2x = f^2(x) > other than f(x) = -x and f(x) = 2x? > -x and 2x are the only two continuous solutions > of f(x)+2x=f(f(x)). > But infinitely many non continuous solutions > exist. > E.g. take any subset A of R such that (t -> -t) > maps A to itself and > (t -> 2t) maps R A into itself, and let f(x) = -x > for x in A and > 2x for x in R A. > -- > Robert Israel > israel@math.MyUniversitysInitials.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada > Hi Robert, > I would rather have my name associated with this > triviality:P=NP as > was proven: > thread/c910051ec44e17c8/9fe84fe28bd2f8f4?lnk=raot#9fe8 > 4fe28bd2f8f4 > MMM And I would rather have you off and go trash another website than trashing this one. === Subject: Re: f(x) + 2x = f(f(x)) William Elliot a .8ecrit : > Are there any solutions, R into R, for > f(x) + 2x = f^2(x) other than f(x) = -x and f(x) = 2x? -x and 2x are the only two continuous solutions of f(x)+2x=f(f(x)). But infinitely many non continuous solutions exist. === Subject: Re: f(x) + 2x = f(f(x)) > William Elliot a .8ecrit : > Are there any solutions, R into R, for > f(x) + 2x = f^2(x) other than f(x) = -x and f(x) = 2x? -x and 2x are the only two continuous solutions of f(x)+2x=f(f(x)). But infinitely many non continuous solutions exist. E.g. take any subset A of R such that (t -> -t) maps A to itself and (t -> 2t) maps R A into itself, and let f(x) = -x for x in A and 2x for x in R A. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: f(x) + 2x = f(f(x)) posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) > Are there any solutions, R into R, for > f(x) + 2x = f^2(x) other than f(x) = -x and f(x) = 2x? Bonjour, Three notices: 1Á) sum(b(i)f^i(x)) = 0 ,b(i)constant, i integer Be r(j) the roots of sum(b(i)*a^i) = 0 , possible solutions on C f(x)= r(j)x . 2Á) One fixed point x=0 , 3Á)a formal relation: from 2x = f^2(x) -f(x) x = {(f-I)/2} o f(x) ,I identity Thence (f-I)/2} = f^ -1 Alain === ignore === Subject: Re: Cantor's argument is erroneous <6E4Rl.29047$ho7.845@newsfe10.iad> [Slightly revised version of an earlier post.] said: > [CM said:] > Ok, on the assumption that you really just don't get it and are not > being disingenuous, I'll give it one last try. The problem (as I and > others have already noted) is that, whether you are able to > acknowledge it youself, to make sense of your own claim about what is > at stake, you yourself have to be presupposing a background language. *Where* specifically did I *insist* we don't have _a_ background > language, when talking about formulas and formal systems? I'll have to admit I only inferred it from the fact that you seemed unwilling simply to say precisely what the language of your theory T was supposed to be. > Didn't I mention in the thread more than one time you can discern a > language from formulas, axioms, given some syntactical conventions > about logical symbols and variable symbols? Perhaps we can in some cases (it will not work for specifying infinite languages), but this is not the convention. For some reason, you want to ignore the fact that your approach is not standard (and not general) and hence you cannot justifiably assume that others are following it. > Why? Because you are talking about a *theory* T. And (as defined by > Shoenfield), a theory is a formal system and, by definition, a formal > system is formal language together with a proof theory, i.e., axioms > + rules of inference. So, just for definitional reason alone, your > reference to a theory presupposes that there is a specific language > in which it is formulated. Now, perhaps that is not what you mean by > theory, but if you wish to communicate with others about > first-order theories, you have to use the conventional definitions > that everyone has agreed upon or, at least, provide alternatives of > your own. So if you are not using the word theory in a way that > presupposes a background language, then you will have to provide an > alternative. Again, Why? what? Er, well: Why do you need explicitly to specify the language of a purported theory? Because: If you only specify axioms without specifying a background language, you don't yet have a theory. So when you talked about your single axiom *theory* T, what you were saying had no fixed meaning (except perhaps for those following your nonstandard convention noted above) because you did not specify the background language. You may have *intended* that it be the language consisting of the non-logical symbols of your axiom -- i.e., as it turns out, the language of pure FOL= -- but, as noted, the universal practice in mathematical logic is to specify one's background theory explicitly; there is no general convention that it can be inferred from a given set of axioms. So you needed to say explicitly what background language you intended in order for your question about the theorems of your theory could be answered. HTH. > Again, my question to you was: >So, what ... does *your* _the language_ there refer to? Well, obviously, I can't answer specifically, of course, because I don't know. It refers to whatever language you intended as the background language for your theory which (according to the conventions of mathematical logic) cannot be inferred from a set of axioms. In case the point is not clear, suppose I know you have several computers of various sorts and you tell me that you have a computer that is acting up and is out of warranty and you ask me where to take it for diagnosis and I reply: An Apple Store, if the computer is a Mac My geek friend Smith, if the computer is a PeeCee. I obviously can't tell you *specifically* what machine the computer refers to there; it refers to whichever of *your* computers you meant. But there is nothing vague about my use of the term. > Obviously you must have had in your mind for it to refer to a > language; Yes indeed, the one you had in mind as the background language for your theory T. > and I might have missed your previous reference to that language (but > isn't that kind of normal in a dialog?). Why do you seem to have > refused answering _that question_, when it was asked simply for the > sake of clarification? Hope the above helps you understand why I, lacking telepathic skills, couldn't give you an exact answer. > If you yourself happened to get confused as to what _that question_ > was about, admit it and I'd rephrase it for clarity. Don't just bury > it by attacking your opponent with something else (e.g. right below) > Otherwise, your claims are literally meaningless and you cannot be > taken seriously. Really, this was by no means intended as an attack. It is just a simple fact that, if you use words that depart from their conventional meanings, claims that use those words are meaningless (more exactly, incapable of being interpreted). > For the nth time, Chris Menzel, my talk of formal system or theory > always includes an assumed background language. And, I guess, I am now to understand that it was the language of pure FOL=. Ok, fine, then I guess the simple answer to your question was NO. There are no theorems of your theory T, in the language of pure FOL=, that contain non-logical symbols not found in the axiom of T. > It's only when such background language is *vacuous* that I claim > would lead us to invalid reasoning. What is a vacuous background language? Please define. > Do you understand my talk now? I think I will if: 1. You define what a vacuous background language is. 2. You acknowledge that the language you intended as the background language for your theory T is the language of pure FOL= that counts = as a logical symbol and contains no non-logical symbols. > And that is why the answer to your question concerning what is at > stake is trivial: > At stake is: if an axiom-set of a T has n non-logical symbols (n > could > be infinite), then can the collection of theorems of T contain new > symbols, whether or not one stipulates these new symbols? > Again: > YES, if the language of T contains symbols not in any axiom of T. > NO, otherwise. > Reply if you want to this, but as I have been doing nothing but > repeating myself trying to get you to understand this elementary > point, > I'm afraid it will be a (further) waste of time to respond again to > you > in this thread. Whether you've perceived you've waisted time isn't my issue here. Well, I decided to waste a little more. :-) I guess I'm still not confused you're a hopeless case, Nam. > You and I have nothing to disagree *about* your No answer here. But > I've always maintained your Yes answer above would lead to invalid > reasoning, which you've never counter that maintaining of mine. I definitely missed any argument to that effect. So you are claiming that the language of a theory cannot contain symbols not found in any axiom of T, on pain of inevitable invalid reasoning? Is that *really* your claim? Since I apparently missed it in earlier rounds, please humor me and show me how it is that assuming (along with Enderton, Mendelson, Schoenfield, etc) (*) The language of a theory T can contain symbols not found in any axiom of T, leads to invalid reasoning. (I'm supposing that (*) is the source of the problem, because it is the only assumption of any substance behind my answer of YES above.) === Subject: Enumerating all Partitionings of a Finite Set Given a positive integer n: Let S(n) be the set {1, 2, ..., n}. We define a Partitioning of S(n) as a set of non-empty subsets of S (n), such that every element of S(n) is an element of exactly one subset. For example, three different Partitionings of S(5) are: { {1, 5}, {2}, {3, 4} } { {1, 2, 4, 5}, {3} } { {1}, {2, 4}, {3}, {5} } We define P(n) as the set of all Partitionings of S(n), and let |P(n)| denote the number of elements of P(n). For example, P(3) = { { {1}, {2}, {3} }, { {1, 2}, {3} }, { {1, 3}, {2} }, { {1}, {2, 3} }, { {1, 2, 3} } } and |P(3)| = 5 Given i, an element of S(|P(n)|): Let F(n,i) be some function that (curries to) provide a bijective mapping from S(|P(n)|) to P(n). For example, some of the values of one possible F(n,i) are: F(1, 1) = { {1} } F(2, 1) = { {1}, {2} } F(2, 2) = { {1, 2} } F(3, 1) = { {1}, {2}, {3} } F(3, 2) = { {1, 2}, {3} } F(3, 3) = { {1, 3}, {2} } F(3, 4) = { {1}, {2, 3} } F(3, 5) = { {1, 2, 3} } F(4, 1) = { {1}, {2}, {3}, {4} } [Q1] What is |P(n)| expressed as a closed form in terms of n? [Q2] Describe in psuedocode a stateless implementation of F(n,i) that completes in no more than O(n) space and O(n) time for arbitrary n and i. -- (This problem statement is an original work of Andrew Tomazos ) === Subject: Re: Enumerating all Partitionings of a Finite Set > Given a positive integer n: Let S(n) be the set {1, 2, ..., n}. We define a Partitioning of S(n) as a set of non-empty subsets of S > (n), such that every element of S(n) is an element of exactly one > subset. For example, three different Partitionings of S(5) are: { {1, 5}, {2}, {3, 4} } > { {1, 2, 4, 5}, {3} } > { {1}, {2, 4}, {3}, {5} } We define P(n) as the set of all Partitionings of S(n), and let |P(n)| denote the number of elements of P(n). For example, P(3) = { > { {1}, {2}, {3} }, > { {1, 2}, {3} }, > { {1, 3}, {2} }, > { {1}, {2, 3} }, > { {1, 2, 3} } > } and |P(3)| = 5 [Q1] What is |P(n)| expressed as a closed form in terms of n? These are the Bell numbers, sequence A000110 at the online encyclopedia of integer sequences, q.v. I think you'll find there isn't a closed form. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Enumerating all Partitionings of a Finite Set > legroups.com>, Given a positive integer n: Let S(n) be the set {1, 2, ..., n}. We define a Partitioning of S(n) as a set of > non-empty subsets of S > (n), such that every element of S(n) is an element > of exactly one > subset. For example, three different Partitionings of S(5) > are: { {1, 5}, {2}, {3, 4} } > { {1, 2, 4, 5}, {3} } > { {1}, {2, 4}, {3}, {5} } We define P(n) as the set of all Partitionings of > S(n), and let |P(n)| denote the number of elements of > P(n). For example, P(3) = { > { {1}, {2}, {3} }, > { {1, 2}, {3} }, > { {1, 3}, {2} }, > { {1}, {2, 3} }, > { {1, 2, 3} } > } and |P(3)| = 5 [Q1] What is |P(n)| expressed as a closed form in > terms of n? These are the Bell numbers, sequence A000110 at the > online > encyclopedia of integer sequences, q.v. I think > you'll find there > isn't a closed form. Isn't this the number of ways of putting n balls in k boxes (with no empty boxes)?. Just use k=1, 2,..,n and add the total?. -- > Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for > email) === Subject: Re: Enumerating all Partitionings of a Finite Set Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) [...] > [Q1] What is |P(n)| expressed as a closed form in terms of n? These are the Bell numbers, sequence A000110 at the online >encyclopedia of integer sequences, q.v. I think you'll find there >isn't a closed form. Right. However, there does exist a remarkable formula (given on the OEIS) that comes close to being a closed form: |P(n)| = exp(-1) * sum_{k>=0} k^n/k! -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Enumerating all Partitionings of a Finite Set <4a19d36a$0$502$b45e6eb0@senator-bedfellow.mit.edu> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.10) Gecko/2009042315 Firefox/3.0.10,gzip(gfe),gzip(gfe) [...] > [Q1] What is |P(n)| expressed as a closed form in terms of n? >These are the Bell numbers, sequence A000110 at the online >encyclopedia of integer sequences, q.v. I think you'll find there >isn't a closed form. Right. However, there does exist a remarkable formula (given on the OEIS) > that comes close to being a closed form: |P(n)| = exp(-1) * sum {k>=0} k^n/k! and there are plenty of finite-but-unbounded sum forms in fact the form you mention can be truncated at 2n and take the next higher integer and there are many finite sums where ugly ops like the next higher integer op are not needed there are also finite recursive relations and the famous generating function ramanujan made many of the first discoveries on these but his work was not well known and later bell and others rediscovered and expanded the theory -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Rotation angle from Rodrigues (Gibbs) representation Hi all. If a have a rotation in the Rodrigues representation, how do I calculate the angle of the rotation? Is it 2atan(||rodrigues||)? === Subject: Re: Rotation angle from Rodrigues (Gibbs) representation > If a have a rotation in the Rodrigues representation, how do I calculate the > angle of the rotation? That angle is supposed to be given. > Is it 2atan(||rodrigues||)? I don't know which norm you are talking about here, but if it is the usual one, then it is equal to 1. If you still want to talk about this, then say exactly what you mean by Rodrigues' representation. Is it this: http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula for instance? Jose Carlos Santos === Subject: Re: JSH: Negative Pell's Equation existence conditions > The existence conditions for non-zero integer solution to j^2 - Dk^2 = > -1, are: 4. If D is divisible by 2 it cannot be divisible by 4. > And if, to the contrary, D is not divisible by 2, _then_ can it be divisible by 4? Mike === Subject: Re: Natural numbers [was: Diagonal wanderings...] > << The dwelling place of meaning is syntax; > semantics is the home of illusion. > As I understand it, for him there are proofs, but no > truths. > http://www.math.princeton.edu/~nelson/papers.html > --> Confessions of an apostate mathematician > By itself, that statement looks pretty stupid to me. > (Perhaps it looks differently in full context.) > Behold semantics: > 1+1=2 > And again: > true ^ false = false > Is it an illusion? > I don't know if the realist view is an illusion. For now, I think as > a realist by nature or habit, but when pressed I become > an agnostic about realism, so I neither deny it or accept it > completely. > One day, Nelson lost the faith in the meaning of mathematical > symbols. > I think of mathematical ideas as residing in human minds, > but to me realism could still be valid, or maybe not > valid. I don't know. Yeah. Mathematical entities surely *seem* real, and naive mathematical > realism is entirely satisfactory for toiling in the mathematical > vineyards. But just as naive epistemological realism (that the world is > WYSIWYG) breaks down when pressed hard (optical illusions, dreams, > hallucinations, etc.), so to does mathematical realism. When pressed, > I'm a hard-core nominalist; but I'm not often pressed. If mathematical truths are discovered, which is pretty much the realist view, this seems to imply a mathematical realm exists, in some she defends Godelian-type realism with a twist of her own ( a detail, perhaps). Cf.: http://www.questia.com/PM.qst?a=o&d=26316369 pages 1 to 3 where she considers some questions raised by realism. http://www.dailygalaxy.com/my_weblog/2008/04/is-mathematics.html presents views of a Platonist, skeptic (?), and anti-Platonist in their own words. ---- I think it's not obvious how to make a convincing account of realism or the mathematical realm. But some parts, say number theory or arithmetical statements, could be part of a realm but maybe not the realm where the continuum hypothesis would have a definite answer. For me, something that matters is that we don't really understand what happens in the brain when we think. Realism is appealing, but hard to justify, in my opinion. David Bernier === Subject: Re: Natural numbers [was: Diagonal wanderings...] <4a132c4a$0$297$b45e6eb0@senator-bedfellow.mit.edu> <4a13924d$0$6675$703f8584@textnews.kpn.nl> <4a157adc$0$6675$703f8584@textnews.kpn.nl> <4a15cb1b$0$1640$703f8584@textnews.kpn.nl> posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) I think it's not obvious how to make a convincing > account of realism or the mathematical realm. But some parts, say number theory or arithmetical > statements, could be part of a realm but > maybe not the realm where the continuum hypothesis > would have a definite answer. For me, something that matters is that we don't really > understand what happens in the brain when we think. Realism is appealing, but hard to justify, in my opinion. I honestly just don't see what the problem is. Computation is entirely physical. Have m pebbles in your left hand and n pebbles in your right; count them all up and you have m+n pebbles. Equivalently you can use a modern computer to do math, or work it out in your head. In no case can you compute anything using supernatural means. Neither math nor logic has anything in it that is not computation. If you believe the pebbles in your hand are real, then you believe the symbol for the number 2 is real. And you do math on the symbol for 2, not the referent of the symbol. The referent doesn't exist in the physical sense, but so what? The referents for E=mc^2 or f = ma or distance = velocity * time don't exist in the physical world either; but does anyone think this amounts to a problem for physical realism? Numbers are an abstraction for quantitative aspects of the physical world. That they are abstract does not mean that they are anything less that completely physically grounded. Marshall === Subject: Re: Natural numbers [was: Diagonal wanderings...] > I think it's not obvious how to make a convincing > account of realism or the mathematical realm. > But some parts, say number theory or arithmetical > statements, could be part of a realm but > maybe not the realm where the continuum hypothesis > would have a definite answer. > For me, something that matters is that we don't really > understand what happens in the brain when we think. > Realism is appealing, but hard to justify, in my opinion. I honestly just don't see what the problem is. Computation is entirely physical. Have m pebbles in > your left hand and n pebbles in your right; count them > all up and you have m+n pebbles. Equivalently you > can use a modern computer to do math, or work > it out in your head. In no case can you compute anything > using supernatural means. Neither math nor logic has anything in it that is not > computation. If you believe the pebbles in your hand > are real, then you believe the symbol for the number > 2 is real. And you do math on the symbol for 2, not > the referent of the symbol. The referent doesn't exist > in the physical sense, but so what? The referents for > E=mc^2 or f = ma or distance = velocity * time > don't exist in the physical world either; but does anyone > think this amounts to a problem for physical realism? Numbers are an abstraction for quantitative aspects > of the physical world. That they are abstract does not > mean that they are anything less that completely > physically grounded. For me, it takes an element of faith to believe in some land of all subsets of the real numbers, for example. Barry Mazur, Mathematical Platonism and its Opposites, EMS Newsletter, June 2008. http://www.ems-ph.org/journals/all_issues.php?issn=1027-488X pp. 19-21 as numbered on the page, or pp. 21-23 in the PDF file. David === Subject: Re: Natural numbers [was: Diagonal wanderings...] <4a157adc$0$6675$703f8584@textnews.kpn.nl> <4a15cb1b$0$1640$703f8584@textnews.kpn.nl> posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > I honestly just don't see what the problem is. [....] For me, it takes an element of faith to believe in some land of > all subsets of the real numbers, for example. Well, ok, that's an example, but it doesn't really illuminate anything for me. And, no offense, it's not a great example. You just mentioned a mathematical construct clearly and uniquely. A better example of something problematic, to my mind, would be a single particular uncomputable real. Barry Mazur, Mathematical Platonism and its Opposites, > EMS Newsletter, June 2008.http://www.ems-ph.org/journals/all issues.php?issn=1027-488X > pp. 19-21 as numbered on the page, > or pp. 21-23 in the PDF file. I had trouble with your URL so I found another one: http://www.math.harvard.edu/~mazur/papers/plato4.pdf I too found it interesting and also more funny that is usual in the math world. (Such dry writers they often are!) But it didn't really seem to have much light to shed. As to invented vs. discovered: it's a false dichotomy. Should we consider the magic constant to be the ratio of a circle's circumference to its diameter or to its radius? The choice is modestly arbitrary; cultural if you will; invented. However one or the other we must surely have: discovered. Euclid's gcd algorith: is it a loop or is it recursive? That's a design question. But the idea was a discovery. Etc. Many individual choices in how we organize our thoughts about math are design questions that could have gone differently historically. But the rules that govern computation are not inventions in the least. To suggest that they are is to suggest that, had things gone differently during the twentieth century, the halting problem might be decidable after all, and that's just silly. I guess I am no closer to seeing the problem. Marshall === Subject: Re: Natural numbers [was: Diagonal wanderings...] ) > I think it's not obvious how to make a convincing > account of realism or the mathematical realm. > But some parts, say number theory or arithmetical > statements, could be part of a realm but > maybe not the realm where the continuum hypothesis > would have a definite answer. > For me, something that matters is that we don't really > understand what happens in the brain when we think. > Realism is appealing, but hard to justify, in my opinion. I honestly just don't see what the problem is. Computation is entirely physical. Have m pebbles in > your left hand and n pebbles in your right; count them > all up and you have m+n pebbles. Equivalently you > can use a modern computer to do math, or work > it out in your head. In no case can you compute anything > using supernatural means. Neither math nor logic has anything in it that is not > computation. If you believe the pebbles in your hand > are real, then you believe the symbol for the number > 2 is real. And you do math on the symbol for 2, not > the referent of the symbol. The referent doesn't exist > in the physical sense, but so what? What does it mean: The referent doesn't exist in the physical sense. ? Do only physical things exist? Where is the referent of red or the referent of connectivity or the referent of liquid? Twoness exist as e.g. roughness exist. There is no essential difference between this two properties. Albrecht > The referents for > E=mc^2 or f = ma or distance = velocity * time > don't exist in the physical world either; but does anyone > think this amounts to a problem for physical realism? Numbers are an abstraction for quantitative aspects > of the physical world. That they are abstract does not > mean that they are anything less that completely > physically grounded. > Marshall === Subject: Re: Natural numbers [was: Diagonal wanderings...] <4a157adc$0$6675$703f8584@textnews.kpn.nl> <4a15cb1b$0$1640$703f8584@textnews.kpn.nl> posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Neither math nor logic has anything in it that is not > computation. If you believe the pebbles in your hand > are real, then you believe the symbol for the number > 2 is real. And you do math on the symbol for 2, not > the referent of the symbol. The referent doesn't exist > in the physical sense, but so what? What does it mean: The referent doesn't exist in the physical > sense. ? In this case, I mean that 2 is not a physical object. You can wander all throughout Europe and Asia, and never find a natural number lying in a pasture, or wedged in the branches of a tree, for example. > Do only physical things exist? Only physical things exist physically. Abstract things exist abstractly. > Where is the referent of > red or the referent of connectivity or the referent of liquid? Exactly my point. > Twoness exist as e.g. roughness exist. There is no essential > difference between this two properties. I completely agree. Marshall === Subject: Re: Natural numbers [was: Diagonal wanderings...] <4a132c4a$0$297$b45e6eb0@senator-bedfellow.mit.edu> <4a13924d$0$6675$703f8584@textnews.kpn.nl> <4a157adc$0$6675$703f8584@textnews.kpn.nl> <4a15cb1b$0$1640$703f8584@textnews.kpn.nl> <4a17a1bb$0$6670$703f8584@textnews.kpn.nl> posting-account=6xUtvgkAAAD_jypmLa2oo2HnrV0e8X9q rv:1.7.13) Gecko/20060414,gzip(gfe),gzip(gfe) > Also: the collection of FOL-sentences that are true in the naturals is > not even PA-definable. > Are you referring to Tarski's theorem re the indefinability of truth? Yes. > How could anyone have a completely rigorous system for that? > I'm not concerned that there are truths about the naturals that are > inaccessible. Agreed. Also: some non-classical logic could work in which not even all > these FOL sentences are expressible. So this second argument is not very > convincing. A possible third argument is as follows: > The idea of the natural number sequence is presumed in the way we define > 'WFF', 'proof', and then also 'consistency'. This brings in circularity: Whenever we have a finite characterization of anything infinite, we > somewhere 'must' invoke a certain extrapolation step ('etcetera', or > '...'), at which point we are relying on the intuition of the natural > number sequence (or equivalently, the intuition of what 'arbitrary > finite iteration' means), making the whole characterization circular. That's a very good point which I have also mentioned sometimes. Naturals are before any thought and being. Any reflection or claiming a theory involves naturals as always there is a first, a second, a third ... . We are not free about defining the naturals as some people claim here. Even the peano axioms uses naturals because there is a first, a second, ..., a fifth axiom, which must be applied in this sequence. In this sense we are not able to define the naturals, we are only free to state them. (And, by the way, the naturals are the numbers I, II, III, ... , and nothing else.) But nobody here ponders about ideas of cranks like me because it is more importend to do crank-bushing, as you call it so nice beneath. I wonder what is the problem of the people who defend an undefendable theory with so much rigor instead of reflecting on it. Albrecht > What bothers me is that we all think we have a simple > mental model of N (with no non-standard crud even getting a look-in). > heads we have some system that generates this, or at least appears to > generate it, (or appears to appear to generate it....) What I'm looking > for is a formal version of that. If there *isn't* a formal version of > that then what sorts of explanations might there be for the apparent > clarity of our mental model? > (IMO, if they weren't so mathematically ignorant, the various cranks > could do far better by digging in this ground than by trying to find > inconsistencies in well-worked-over areas.) You have no idea how warmheartedly i agree with you. > But allow me to add that the various crank-bashers could also spend > their time better digging into this than by trying to convince cranks. The true master learns from the biggest fool > But, once again: proven is too much said. (Depends also a bit on what > you're going to call 'entirely rigorous', of course.) > But all of this is a bit of an irrelevant detail in my story, isn't it? > For sure. I just took the opportunity to branch the thread into an area > that interests me more. > -- > Herman Jurjus === Subject: Re: Natural numbers [was: Diagonal wanderings...] <4a132c4a$0$297$b45e6eb0@senator-bedfellow.mit.edu> <4a13924d$0$6675$703f8584@textnews.kpn.nl> <4a157adc$0$6675$703f8584@textnews.kpn.nl> <4a15cb1b$0$1640$703f8584@textnews.kpn.nl> <4A17E45A.3CC0069D@gmail.com> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > If we define: > 1 is a natural number > and > with n also n+1 is a natural number > and > N is the smallest set that satisfies both conditions > then N is uniquely specified. > Of course there can be different models for N and there can be > different names for the elements of N. But that does not matter. The > natural numbers do not enter mathematics because someone defines > them, names them, or makes models of them, but because the natural > numbers are simply existing and mathematics is built upon them. > Suddenly, WM the realist/platonist. Did *not* see that coming. > -- > hz But in virtually the same breath, WM will also deny that any such N can > exist. At least in his world. Of course N = 1, 2, 3, ... exists (if refraining from considering physical constraints, as is usual in sci.logic). Otherwise I could not use it. But it does not exist, as you may erroneously believe, as an actually infinite set. If n is a natural then n + 1 is a natural does not mean that every n is already existing. If n is recognized as a natural number === Subject: Re: Curvature of spacetime (...) Dono, you are the troll exposed in USENET so easy because you LACK a BRAIN and could not see the trap that any 5 years-old child could :-D Dono, you are the troll who failed, for six months, to solve a simple exercise to obtain the relativistic Hamiltonian, even when you were given the SOLUTION and the details of the computation are available in any TEXTBOOK :-D Dono, you are the troll with more than 50 nonsensical editions of You are the troll who got a specific section in Wikipedia devoted to your nonsenses, because you are a PRETENDER :-D Dono, don't forget you were banned by administrators due to your DICTATORSHIP attempts to falsify public ratings voting by yourself, and your several hundred of fake votes deleted :-D http://canonicalscience.blogspot.com/2008/08/some-samples-of-usenet-fauna- iii-nasty.html http://canonicalscience.blogspot.com/2008/12/catching-big-troll.html -- http://www.canonicalscience.org/ Usenet Guidelines: http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html === Subject: Re: Curvature of spacetime posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP On May 24, 4:53 pm, Juano R. Gonz.87lez-'lvarez > Guidelines:http://www.canonicalscience.org/en/miscellaneouszone/guidelines.h t ml Hypocritical cunt. === Subject: Construction of the extended binary Golay code posting-account=HtkKKgkAAADgQ0udlYS7dER9B-VwWupX Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) I would appreciate any suggestion regarding the following problem. I'm trying to write a simple and fast program to generate all code words of the extended binary Golay code. Wikipedia (http:// en.wikipedia.org/wiki/Binary Golay code) gives 5 different constructions, but I don't know which one would be the simplest one. I should mention that I am quite ignorant in this topic, so I do not entirely understand those constructions, but I will be OK, as long as I know on which construction I should concentrate. A more explicit construction is shown in http://en.wikipedia.org/wiki/Steiner system in the context of the Steiner system S(5, 8, 24). The idea is to write down sequences of 24 bits in lexicographic order, missing out any one which differs from some earlier one in fewer than 8 positions. It seems that it would require comparisons to all previously created sequences, which seems a lot. So, I guess my question comes to whether one of the 5 constructions in (http://en.wikipedia.org/wiki/Binary Golay code) is more explicit, and would require fewer calculations. === Subject: Re: Does anybody actually use graphing calculators to do something useful? posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > important to science. Make a graph of y = x^2, but point the 'y' values in the -y direction. You'll draw a down-turned parabola. The one I drew was d = t^2, the velocity curve of falling objects. Studying such, I realized that the rate of change of the velocity with respect to time is LINEAR, or uniform. The Law of the Conservation of Energy says: Energy IN must = energy OUT. Studying that down-turned parabola I realized that accelerations like 'g' can only be caused by a UNIFORM downward force. Since the velocity is accruing LINEARLY for falling objects, then the momentum and kinetic energy (the same things) must be accruing LINEARLY, too! KE must be increasing as the DISTANCE of fall. Einstein accepted that notion to write his erroneous E = mc^2. But KE can only be increasing LINEARLY. That's because all simple accelerations have only one uniform force acting (like the object's weight). Einstein's notion: There isn't enough energy in the entire Universe to cause even a speck of matter to travel to velocity 'c'. was because he didn't know that 'g' isn't an exponential quantity! Galileo and Newton thought 'g' = 32 feet per second SQUARE. Einstein, nor most dunce scientists today, don't know that the equation should have been: 'g' = 32.174 feet per second EACH second. That way the implied force is uniform, and the velocity increases linearly. The above may not seem very important to you, but such fact disproves Einstein's Special Theory of Relativity! So, study the parabola and you should understand this new science truth! NoEinstein I am like most technonerds and I find doing graphs of functions on my > calculator kind of fun when i am sitting around somewhere with nothing > to do. I thought they were incredible the first time I saw them back > in the 80's and I desperately wanted one. Now they are all over the > place and all my students have them as do I. Nevertheless, thinking > over the last 30 years of my teen and adult life I can't actually > think of one case where I have used one to solve a problem in a lab, > to do homework, to teach a lesson, or even better intuit a problem > that had been bugging me. If I want to graph something simple, i do it on paper, harder, I do it > on a computer. In my experience, there is no middle ground that > graphing calculator actually do better than computers or paper, > largely because computers and paper are ubiquitous. Another thing I > have noticed about graphing calculators is a lot of the time they have > sacrificed other functionality or pushed other functionality to the > side that makes them harder to use for the kinds of operations most > scientists and teachers actually need. Texas instruments makes a big > deal about its graphing and data manipulation abilities (arrays, > matrices, statistics), but in my experience, I never wind up using > those functions because they are not worth the hassle. Recently, I have again become a fan of Casio Calculators. No graphing > but good editing and replay capabilities as well as symbolic > processing (very useful). It is very nice to enter problems in, in > terms of fractions, radicals, pi, e, etc.. and see the answers come > out in the same terms. I particularly like this in teaching where it > helps students visualize the structure of fractions and ratios, see > crunching everything down to intuitively barren decimal > approximations. Without, the overhead of graphing these calculators > can put more useful things in easy to access places and squeeze in > things like definite integrals. Finally, non-graphing calculators are > a hell of a lot cheaper. My Casio fx-155 es cost me about 20 dollars > while my TI-84 plus, silver edition cost me about 100. I use the Casio > all the time and use the TI only when i have misplaced the Casio or > want to play a game. I am recommending the Casio to all my students. Anyway, I was wondering if my experience is typical. Anybody agree > with my experience or instead find they use their graphing features > all the time. In case anybody is wondering, I have no vested interest in either > Casio or TI. Search my usenet history, you will see this is true. === Subject: Re: Does anybody actually use graphing calculators to do something useful? > [ a mercifully short manifesto, but again about the same damn' thing ] Oh, lighten up already! The OP was reminiscing fondly about scientific calculators. It's kind of fun. We've all had them. Must you turn even this into an opportunity to climb up on a soap box and preach? This is as bad as dealing with the Holy Rollers in Appalachia. Just because two or more people are forgathered does not mean they're here to hear a loony sermon or some guy speaking in tongues. On the contrary. Believe it or not, it is *not* all about you. Do svidaniya. -- RLW === Subject: Re: Does anybody actually use graphing calculators to do something useful? > I am like most technonerds and I find doing graphs of functions on my > calculator kind of fun when i am sitting around somewhere with nothing > to do.... Once bought a Casio calculator with a 2 monochrome display, used for plotting. Honestly never did all that much with it as the things for which I needed graphs weren't usually functions, but datasets. Did program it to display a Mandelbrot set, though. After running the convergence test interval up far enough to produce a decent-looking one, it took all day to complete the plot. Still, it was pretty. Never used it much, though. It was a good piece of gear for what it was, but the keyboard was so difficult to use that I always went instead to the nearest available computer for what I needed. (Minis, back then.) It's still here, packed in a box probably. If it had an IR port through which it could talk to a keyboard, I'd likely still use it. (This from a guy who uses a Life Drive and folding keyboard as a word processor.) -- RLW === Subject: Re: Does anybody actually use graphing calculators to do something useful? I am like most technonerds and I find doing graphs of functions on my > calculator kind of fun when i am sitting around somewhere with nothing > to do.... Once bought a Casio calculator with a 2 monochrome display, used for > plotting. Honestly never did all that much with it as the things for > which I needed graphs weren't usually functions, but datasets. Did program it to display a Mandelbrot set, though. After running the > convergence test interval up far enough to produce a decent-looking one, > it took all day to complete the plot. Still, it was pretty. Never used it much, though. It was a good piece of gear for what it was, > but the keyboard was so difficult to use that I always went instead to > the nearest available computer for what I needed. (Minis, back then.) It's still here, packed in a box probably. If it had an IR port through > which it could talk to a keyboard, I'd likely still use it. (This from a > guy who uses a Life Drive and folding keyboard as a word processor.) -- RLW The HP49/50 series can do some reasonably serious math with the various libraries that are available for it at hpcalc.org, q.v. -- Virgil === Subject: Re: Does anybody actually use graphing calculators to do something useful? Anyway, I was wondering if my experience is typical. Anybody agree > with my experience or instead find they use their graphing features > all the time. I've never used a graphing calculator, but I have made some use of the graphing functions in Microsoft Excel. I rather doubt that a calculator supports the graphing functions of Excel. This led to an amusing incident one day. I was asked to clean up a report written by a member of the research staff, based on data collected by another staff member. The report had a graph in it, and something didn't seem quite right about it. The data points each had two coordinates, and the graph was labelled on the axes with the coordinates of each point. But I measured the distance between points along the equidistant, but the X-coordinates were not equidistant in the original data set. Some of the deviations were large enough you should have been able to see them visually, which is what aroused my suspicion. I obtained the original Excel file, and discovered that the wrong XY plot mode was chosen. The chosen mode assumes that all data points are equidistant in X. It only uses the X coordinate data to label the points. The proper mode also uses this data to position the points in X. I applied the correct mode, and suddenly the graph looked considerably different. This graph was being used to determine parameters in experimental processes, so I immediately walked over to the office of the original researcher to show her the two plots, just in case she was using the wrong one. It turned out, she hadn't even seen the draft report prepared by her assistant. She already had the data, so she didn't have time to review a report on the same data. But she did know exactly what I was talking about, and she reached over for the notebook that contained her notes of that experiment. She turned right to the page with her version of the plot, done in pencil on graph paper and taped into the notebook, and of course it looked just like the one I had generated using the correct graphing mode. I suppose the lesson is that sometimes the tools can be more sophisticated than the user. Or sometimes the simplest tools are the best. Graph paper doesn't lie. === Subject: Re: Does anybody actually use graphing calculators to do something useful? . . . > Recently, I have again become a fan of Casio Calculators. No graphing > but good editing and replay capabilities as well as symbolic > processing (very useful). It is very nice to enter problems in, in > terms of fractions, radicals, pi, e, etc.. and see the answers come > out in the same terms. I particularly like this in teaching where it > helps students visualize the structure of fractions and ratios, see > crunching everything down to intuitively barren decimal > approximations. Without, the overhead of graphing these calculators > can put more useful things in easy to access places and squeeze in > things like definite integrals. Finally, non-graphing calculators are > a hell of a lot cheaper. My Casio fx-155 es cost me about 20 dollars > while my TI-84 plus, silver edition cost me about 100. I use the Casio > all the time and use the TI only when i have misplaced the Casio or > want to play a game. I am recommending the Casio to all my students. > . . . The calculator sitting next to my keyboard is a Casio fx-7400G PLUs POWER GRAPHIC. Yes, Casio makes graphing calculators--at least they used to. A quick Google search shows they still do, several models, including mine. The list price for today's version of mine (the picture looks slightly different) is $39.99, and I'm pretty sure I could find if for substantially less. But I have to agree with the OP about one thing: I was thrilled with the prospect of getting a graphing calculator, but I don't use that capability very much. Not very much doesn't mean never, however. It is sometimes very handy to see a plot of data points, and in some cases functions. What I use it more for (other than simply as a calculator) is to run a few SIMPLE programs. === Subject: Re: Does anybody actually use graphing calculators to do something useful? posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > I am like most technonerds and I find doing graphs of functions on my > calculator kind of fun when i am sitting around somewhere with nothing > to do. I thought they were incredible the first time I saw them back > in the 80's and I desperately wanted one. Now they are all over the > place and all my students have them as do I. Nevertheless, thinking > over the last 30 years of my teen and adult life I can't actually > think of one case where I have used one to solve a problem in a lab, > to do homework, to teach a lesson, or even better intuit a problem > that had been bugging me. If I want to graph something simple, i do it on paper, harder, I do it > on a computer. In my experience, there is no middle ground that > graphing calculator actually do better than computers or paper, > largely because computers and paper are ubiquitous. Another thing I > have noticed about graphing calculators is a lot of the time they have > sacrificed other functionality or pushed other functionality to the > side that makes them harder to use for the kinds of operations most > scientists and teachers actually need. Texas instruments makes a big > deal about its graphing and data manipulation abilities (arrays, > matrices, statistics), but in my experience, I never wind up using > those functions because they are not worth the hassle. Recently, I have again become a fan of Casio Calculators. No graphing > but good editing and replay capabilities as well as symbolic > processing (very useful). It is very nice to enter problems in, in > terms of fractions, radicals, pi, e, etc.. and see the answers come > out in the same terms. I particularly like this in teaching where it > helps students visualize the structure of fractions and ratios, see > crunching everything down to intuitively barren decimal > approximations. Without, the overhead of graphing these calculators > can put more useful things in easy to access places and squeeze in > things like definite integrals. Finally, non-graphing calculators are > a hell of a lot cheaper. My Casio fx-155 es cost me about 20 dollars > while my TI-84 plus, silver edition cost me about 100. I use the Casio > all the time and use the TI only when i have misplaced the Casio or > want to play a game. I am recommending the Casio to all my students. Anyway, I was wondering if my experience is typical. Anybody agree > with my experience or instead find they use their graphing features > all the time. In case anybody is wondering, I have no vested interest in either > Casio or TI. Search my usenet history, you will see this is true. ---------------- the only calculator i used in building my mode was a simple Casio pocket calculator !!!! Ohh i quite forgot i used my creative imagination and chemical physics nuc physics 3d geometric structues as i aquiled in decades of ed work and skills with 3d structures and endless trial and error calculations and a remark to the op poster : (shocking news ??? (:-) most physical entities are 3d structures and not flat paper structures !! they are not even graphs ............ ATB Y.Porat ------------ === Subject: Re: Does anybody actually use graphing calculators to do something useful? posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009052115 Gentoo Firefox/3.0.10,gzip(gfe),gzip(gfe) > I am like most technonerds and I find doing graphs of functions on my > calculator kind of fun when i am sitting around somewhere with nothing > to do. I thought they were incredible the first time I saw them back > in the 80's and I desperately wanted one. Now they are all over the > place and all my students have them as do I. Nevertheless, thinking > over the last 30 years of my teen and adult life I can't actually > think of one case where I have used one to solve a problem in a lab, > to do homework, to teach a lesson, or even better intuit a problem > that had been bugging me. > If I want to graph something simple, i do it on paper, harder, I do it > on a computer. In my experience, there is no middle ground that > graphing calculator actually do better than computers or paper, > largely because computers and paper are ubiquitous. Another thing I > have noticed about graphing calculators is a lot of the time they have > sacrificed other functionality or pushed other functionality to the > side that makes them harder to use for the kinds of operations most > scientists and teachers actually need. Texas instruments makes a big > deal about its graphing and data manipulation abilities (arrays, > matrices, statistics), but in my experience, I never wind up using > those functions because they are not worth the hassle. > Recently, I have again become a fan of Casio Calculators. No graphing > but good editing and replay capabilities as well as symbolic > processing (very useful). It is very nice to enter problems in, in > terms of fractions, radicals, pi, e, etc.. and see the answers come > out in the same terms. I particularly like this in teaching where it > helps students visualize the structure of fractions and ratios, see > crunching everything down to intuitively barren decimal > approximations. Without, the overhead of graphing these calculators > can put more useful things in easy to access places and squeeze in > things like definite integrals. Finally, non-graphing calculators are > a hell of a lot cheaper. My Casio fx-155 es cost me about 20 dollars > while my TI-84 plus, silver edition cost me about 100. I use the Casio > all the time and use the TI only when i have misplaced the Casio or > want to play a game. I am recommending the Casio to all my students. > Anyway, I was wondering if my experience is typical. Anybody agree > with my experience or instead find they use their graphing features > all the time. > In case anybody is wondering, I have no vested interest in either > Casio or TI. Search my usenet history, you will see this is true. ---------------- > the only calculator i used in building my mode > was a simple Casio pocket calculator !!!! Ohh i quite forgot > i used my creative imagination > and chemical physics nuc physics > 3d geometric structues > as i aquiled in decades of ed work > and skills with > 3d structures and endless > trial and error calculations ...and you still can't calculate the spectrum of the Hydrogen atom. and a remark to the op poster : > (shocking news ??? (:-) > most physical entities are > 3d structures and not flat paper structures !! > they are not even graphs ............ ATB > Y.Porat > ------------ === Subject: Re: Does anybody actually use graphing calculators to do something useful? posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > I am like most technonerds and I find doing graphs of functions on my > calculator kind of fun when i am sitting around somewhere with nothing > to do. I thought they were incredible the first time I saw them back > in the 80's and I desperately wanted one. Now they are all over the > place and all my students have them as do I. Nevertheless, thinking > over the last 30 years of my teen and adult life I can't actually > think of one case where I have used one to solve a problem in a lab, > to do homework, to teach a lesson, or even better intuit a problem > that had been bugging me. > If I want to graph something simple, i do it on paper, harder, I do it > on a computer. In my experience, there is no middle ground that > graphing calculator actually do better than computers or paper, > largely because computers and paper are ubiquitous. Another thing I > have noticed about graphing calculators is a lot of the time they have > sacrificed other functionality or pushed other functionality to the > side that makes them harder to use for the kinds of operations most > scientists and teachers actually need. Texas instruments makes a big > deal about its graphing and data manipulation abilities (arrays, > matrices, statistics), but in my experience, I never wind up using > those functions because they are not worth the hassle. > Recently, I have again become a fan of Casio Calculators. No graphing > but good editing and replay capabilities as well as symbolic > processing (very useful). It is very nice to enter problems in, in > terms of fractions, radicals, pi, e, etc.. and see the answers come > out in the same terms. I particularly like this in teaching where it > helps students visualize the structure of fractions and ratios, see > crunching everything down to intuitively barren decimal > approximations. Without, the overhead of graphing these calculators > can put more useful things in easy to access places and squeeze in > things like definite integrals. Finally, non-graphing calculators are > a hell of a lot cheaper. My Casio fx-155 es cost me about 20 dollars > while my TI-84 plus, silver edition cost me about 100. I use the Casio > all the time and use the TI only when i have misplaced the Casio or > want to play a game. I am recommending the Casio to all my students. > Anyway, I was wondering if my experience is typical. Anybody agree > with my experience or instead find they use their graphing features > all the time. > In case anybody is wondering, I have no vested interest in either > Casio or TI. Search my usenet history, you will see this is true. > ---------------- > the only calculator i used in building my mode > was a simple Casio pocket calculator !!!! > Ohh i quite forgot > i used my creative imagination > and chemical physics nuc physics > 3d geometric structues > as i aquiled in decades of ed work > and skills with > 3d structures and endless > trial and error calculations ...and you still can't calculate the spectrum of the Hydrogen atom. > and a remark to the op poster : > (shocking news ??? (:-) > most physical entities are > 3d structures and not flat paper structures !! > they are not even graphs ............ > ATB > Y.Porat > ------------ no need !! no need to solve all the problems of this word at once !!! no one ever did it before (solved all the problems of the world) my work as a start up is unprecedented !! and will get into the history of science whether you like it or able to understand it or not !!! 2 you are not in a position to judge my work and my contributions here !! especially because you are not an honest generous or may be a mature enough person !!! Y.P -------------------------- === Subject: Re: Relativity Cranks versus Quantum Geniuses This problem only arises for those who kneel on the altar of > relativity. Hey Strich baby--what's your problem with general relativity. There > has yet to be an observation that contradicts predictions of relativity. > It is a fruitful tool for cosmology and it is incorporated in the > systems. So what's you problem Strich? Locality, nonlocality--what do these > have to do with relativity? that makes that argument that the universe is non-local as > was assumed by Einstein... but I would like to point out > that that argument is far from over--and that, so far, special > relativity is holding its own. > Quantum-mechanical wave functions cannot > be represented mathematically in anything smaller > than a mind-bogglingly high-dimensional > space called a configuration space. If, as some argue, > wave functions need to be thought of as concrete > physical objects, then we need to take seriously > the idea that the world's history plays itself > out not in the three-dimensional space of our everyday > experience or the four-dimensional spacetime > of special relativity but rather this gigantic > and unfamiliar configuration space, out of which > the illusion of three-dimensionality somehow > emerges. Our three-dimensional idea of locality > would need to be understood as emergent as well. > The nonlocality of quantum physics might be > our window into this deeper level of reality. The status of special relativity, just more than > a century after it was presented to the world, is > suddenly a radically open and rapidly developing > question. This situation has come about because > physicists and philosophers have finally followed > through on the loose ends of Einstein's longneglected > argument with quantum mechanics > an irony-laden further proof of Einstein's genius. > The diminished guru may very well have been > wrong just where we thought he was right and > right just where we thought he was wrong. We > may, in fact, see the universe through a glass not > quite so darkly as has too long been insisted. Stay tuned! Much of our thinking about physics uses optional models. The notion that light traverses a three dimensional interval is one of these. We never observe light in transit. Light as observed is an interaction between two physical objects and the interval between the transitions in the two objects is zero. This is implicit in the theory of special relativity. -- Michael Press === Subject: Re: Relativity Cranks versus Quantum Geniuses > Stay tuned! Much of our thinking about physics uses optional models. > The notion that light traverses a three dimensional interval > is one of these. We never observe light in transit. Light > as observed is an interaction between two physical objects > and the interval between the transitions in the two objects > is zero. This is implicit in the theory of special relativity. > You say the interval between transitions in the two objects is zero? How come I can fire a laser at a corner reflector on the moon and get some photons back, taking about 2.5 seconds? === Subject: Re: Relativity Cranks versus Quantum Geniuses > Stay tuned! Much of our thinking about physics uses optional models. > The notion that light traverses a three dimensional interval > is one of these. We never observe light in transit. Light > as observed is an interaction between two physical objects > and the interval between the transitions in the two objects > is zero. This is implicit in the theory of special relativity. > You say the interval between transitions in the two objects > is zero? Yes, I do. ds^2 = c^2.dt^2 - dx^2 - dy^2 - dz^2 = 0 for two events on a light cone. > How come I can fire a laser at a corner reflector on the moon > and get some photons back, taking about 2.5 seconds? delta t = 2.5 second. -- Michael Press === Subject: Re: Relativity Cranks versus Quantum Geniuses Much of our thinking about physics uses optional models. The notion > that light traverses a three dimensional interval is one of these. We > never observe light in transit. Light as observed is an interaction > between two physical objects and the interval between the transitions > in the two objects is zero. This is implicit in the theory of special > relativity. > You say the interval between transitions in the two objects is zero? How come I can fire a laser at a corner reflector on the moon and get > some photons back, taking about 2.5 seconds? I suspect he means the spacetime interval. For light, that IS zero. (Spacetime interval)^2 = (time )^2 - (distance)^2 Since the distance that light travels, expressed in time units, is the same as the time of travel, light always has a zero spacetime interval. Think of it this way: if X is the distance traveled in light years, then the time for light to travel is X years. So, X^2 -X^2 = 0, always. To go from earth to the corner cube and back is 2.5 light-seconds. === Subject: Re: look over my math posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.13~pre080614i-0etch1),gzip(gfe),gzip(gfe) > If you are interested in math, I invite you to visit my web site and look > through my work. Admitedly some of it is wrong (dead wrong), but I'll let you figure it out. > On the other hand, some of it is correct (actually right), and are useful > tools for further developments. For instance, I haven't solved the quartic, but I have solved the > triangulation method used for GPS. I don't use math in my profession (janitor), but I use it as therapy for > whatever ails me (mental illness). It is a healthy activity that brings > valor to my life. http://mypeoplepc.com/members/jon8338/math/index.html Jon G. I took a look around some of your site. The circle with the moving central nodes is kind of annoying to me. It came up in the inversion tensors page. I didn't try to follow all your equations but it is nice to see someone doing out the work in graphics. What software tools do you use? Here is some math you might enjoy. It comes from a simple place, though it can get complicated quickly: http://bandtechnology.com/PolySigned/index.html Polysign needs quite a bit of development and alot of standard mathematicians don't like polysign, so it's an area I invite you to explore in the hope of gaining some contribution from you. - Tim === Subject: Re: look over my math > If you are interested in math, I invite you to visit my web site and > look through my work. Admitedly some of it is wrong (dead wrong), but I'll let you figure > it out. On the other hand, some of it is correct (actually right), > and are useful tools for further developments. For instance, I haven't solved the quartic, but I have solved the > triangulation method used for GPS. I don't use math in my profession (janitor), but I use it as therapy > for whatever ails me (mental illness). It is a healthy activity that > brings valor to my life. http://mypeoplepc.com/members/jon8338/math/index.html Jon G. Hey, if you enjoy it and find it rewarding, go for it. Nice work so far. === Subject: Re: look over my math If you are interested in math, I invite you to visit my web site and look > through my work. Admitedly some of it is wrong (dead wrong), but I'll let you figure it out. > On the other hand, some of it is correct (actually right), and are useful > tools for further developments. For instance, I haven't solved the quartic, No need. It's been done. > but I have solved the > triangulation method used for GPS. I don't use math in my profession (janitor), but I use it as therapy for > whatever ails me (mental illness). It is a healthy activity that brings > valor to my life. http://mypeoplepc.com/members/jon8338/math/index.html Jon G. -- ... when we came back, late, from the hyacinth garden, Your arms full, and your hair wet, I could not Speak, and my eyes failed... === Subject: Re: Diagonal wanderings (incongruent by construction) ... > Sorry, it cannot be proven in ZFC but it can be proven in mathematics, > that any vertical line can be matched in length by a horizontal line. > For every lenght(H) there is a length(B) such that length(B) >= length > (H) > > What part of mathematics? Try it in Euclidean geometry. Use Cartesian > coordinates. Origin is (0, 0); line 1 is y = 0, line 2 is y = x. Which > line is the base of this triangle? Your example is similar to this. For > each n, we have the triangle with origin (0, 0), a segment to (0, n) and > a segment to (n, n) with a base connecting (0, n) and (n, n). What is the > base if line 1 and line 2 become lines without bounds? So we have here a > triangle with two infinite sides and no third side. > > If all the points of the two side are there, then all the points of > the third side are there. Why? What is the function of that third line? > If two sides become lines without bounds, what becomes the third > side? Does it disappear suddenly. Yes, if infinity does not exist, if > omega is not a possible coordinate, then there is no third line, but > then there are neither complete base and diagonal. The coordinate omega indeed does not exist. But do you not allow half-lines as complete entities? > If however omega > exists and even omega + 1, and so on, then we have all three corners > and all three lines. Omega does exist, but is not used as a coordinate. > Either actual infinity exists for all lines or for none. You either view half-lines as complete, or not. > In geometry we don't refer to gravity. If there is an angle with > completely existing fixed lines, then there is also the third side of > the corresponding triangle. > > What is the third side in the triangle I described above? > > There is no third side because there is no actual infinity. My proof > uses modus tollens: > If there is actual infinity then there is a third side and there is no > third side. Why? You do not accept an angle with completely existing half-lines? What parts of the half-lines are missing? > In other words, if there can be an actually infinite height, then the > existence of an actually infinite base cannot reasonably beexcluded, > without referring to general relativity. > > Eh? What has general relativity to do with this discussion? I thought it > was about mathematics. > > I did so too, but t seems that you distinguish lines parallel to > gravity and perpendicular to it. Where did I mention gravity? What are lines parallel to gravity? I have no idea what you are talking about. As far as I know I am talking mathematics. > Again avoiding the question. I ask about > for each digit in the diagonal there are lines that contain it > and there are lines that do not contain it > isn't > there is a line that contains all digits of the diagonal > in direct contradiction to the first? Or how is it possible that > there are lines that do not contain it > does not conflict with > there is a line that contains all digits of the diagonal? > > Of course there is a conflict. It stems from the assumption of a > finished infinite diagonal. > > No, it stems from what you think a finished infinite diagonal actually does > mean. So you do not understand ZF. > > You do not claim that every point (or every digit) of the diagonal > does exist? Again avoiding the question. Why do you not just answer the question posed? > Obviously not.The decimal expansion of 1/33 does only comprise one > point, namely that behind the leading zero. Did you really not know > that? > > Eh? So the decimal expansion of 1/33 is 0.? A bit of clarity can help at > times. > > The decimal expansion does comprise numbers and *one* point. The > decimal expansion of 1/33 *begins* as 0.030303, and it continues like > that, but it contains only one decimal point and no further points. It > is not 0.030303..., and I don't remember that I ever happened to see > it. So apparently you do not know what the ... actually does mean. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Diagonal wanderings (incongruent by construction) Nntp-Posting-Host: hera.cwi.nl ... > What numbers can be written by your abstract machine? Does it > write natural numbers or abstract numbers? > > In mathematics natural numbers are abstract. > > And machines too. But the abstract numbers writen by an abstract > machine can be are witten as concrete sequences of decimals or bits. > So why do you not start with the largest? > > In the abstract machine there is no largest. So how can we start with > something that does not exist? > > Consider only those that can be written and therefore exist. In the abstract machine each natural number can be written, and therefore exists. You are deviating from abstraction. > Take the > largest of those. If you are in dispair, start with 1, 2, 3, ..., > 10^10. Certainly they can be written. Take 10^10 then. Continue as > long as is possible without having the machine explode. And spare us > with the silly method to begin always at 1 again. You do so only in > order to hide the incapability of really writing all naturals. Everything concrete in here, nothing abstract. > Eh? It is an abstract machine. > > Even abstract machines can be excluded to exist, if they cannot do > what they can do, or vice versa. > > I do not understand. This is not mathematics, I think. > > Yes. Here you are right! Aha, you do not understand yourself either! [ About the number 'n' where Li(x) - pi(x) changes sign.] > I ask you whether it does exist or not. Not whether it exists as a > sequence of digits. Why do you evade the questions asked? > > This number does exist as an idea. But presently this number seems > to resemble rather an interval than what we usually call a number. > Doesn't matter. This same fate it shares with pi and other numbers. You have a very strange view on mathematics. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Diagonal wanderings (incongruent by construction) Axiom of Infinity (which WM calls the Axiom of _Actual_ Infinity in > order to distinguish it from his new axiom) of ZF with this axiom There is no need for any such axiom to be added to ZF-I: the usual von Neumann model of naturals remains valid, and the proposed axiom is a theorem. - Tim === Subject: Re: Diagonal wanderings (incongruent by construction) Nntp-Posting-Host: hera.cwi.nl > I say the function f(x) has coarse continuity, if > |f(y) - f(x)|/|y-x| < C > for |y-x| > 1 and a fixed positive constant C. > Coarse continuity prevents that a function in the infinite behaves > completely different from its behaviour for finite arguments. > > Can you prove that? > > Of course. If > f(omega) = LIM [y --> omega] f(y) > should deviate by an infinite value from every f(n), n in N, > we have |f(omega) - f(n)| > C for every C in R. > > Yes, that is true if f(omega) is indeed equal to the limit. What if > f(omega) is *not* equal to the limit? > > Then N must contain something that causes this deviation. Why? The explanation is pretty simple. N does not have a last element and omega does not have a predecessor. > You have to prove that it actually is equal > to the limit. > > I assume that omega is the limit of all FISONs. That is just the case > if it is the set of all natural numbers. Depends on how you define limit. With a common definition of limits on sets you will have: lim{n -> oo} FISON(n) = N but also: lim{n -> oo} {n} = {}. But this is neither here nor there, you do not have to prove that omega is a limit, you have to prove that f(omega) is actually equal to the limit of f(n). > You are again assuming what has to be proven: that f(omega) > is equal to the limit. What reason do you have to expect that the > function at a limit point is equal to the limit of the function? > > Omega is the limit of all finite sequences of natural numbers because > there is nothing else but natural numbers that make up N. Should f > (omega) differ from the limit, then N must contain soemthing else than > natural numbers or coarse continuity must be violated. Try again, this is correct, but you have to prove that the function is course continuous. You can prove *that* only when you prove that f(omega) is the limit. And to prove that you can not use course continuity, because that is what you wish to prove. When two properties are equivalent when you need to prove one of the properties you can not use the other property unless you have already proven that that does hold. > > The function 2n/n for n in N has coarse continuity. > > I would even state that it is continuous and not defined for any > infinite n. > > It is a function that is only defined for natural numbers, hence it > is not continuous. A function cannot be continuous where it is > undefined. BTW, I do not state that it is continuous everywhere, I say only that it can be stated that it is continuous for each n in N. There are ways to also define continuity for functions from N, and they are commonly used. > Right. So you can not express any expectations about that function at > omega. > > But at that point where all natural numbers are collected in the set N > with cardinality |{1, 2, 3, ...}|. That is omega. The function is not defined at that point, so you can not conclude anything about continuity there. Or, what 'n' should I will in the formula '2n/n'? > Apparently you do not know it. There are various definitions, > the most common is that it is not equal to 0 (as an ordinal number) > and also does not have a predecessor. > > Apparently you do not know it. Your ramblings do not explain _why_ a > number is called limit ordinal but are a mere description of some > numbers _that_ are called limit ordinal. (That had already been > stated by Cantor.) > > Oh, well, apparently you are stuck with mathematics at the time of > Cantor and did not follow anything after that. In current mathematics > it is called limit number because you can not get there by single steps. > > Oh, that is not different from Cantor's time. But the name comes from > the expectation that you can get there by many single steps. Nope. Not in current mathematics. > If it > were completely inaccessible, it should be called inaccessible > ordinal. But why then should it be accessible by the magic: go > there, take all steps together? Apparently you do not know the terminology. Something is a limit ordinal if and only if you can not get there by the successor operation from other ordinals. I think that inaccessible ordinal is in many ways synonymous to limit ordinal. But it is false that there is a magic go there, take all steps together. The axiom of infinity states that an inductive set does exist, it is not talking about steps at all. It is your thinking that in someway steps are thrown in together is wrong. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Diagonal wanderings (incongruent by construction) ... > But there is no proof. Moreover, you are confusing the issue using lines. > Exactly the same argument can be stated about natural numbers: > If all natural numbers are subject to investigation and if there are > not two equal, then one must be the largest. > > Of course. But you state such without proof. > And that one is trivially false in ZF. Because the axiom of infinity > explicitly states that there is a set that has no largest element and > that has no two elements equal to each other. > > Therefore the axiom of infinity is wrong, it leads to contradiction > with mathematics. That is false, because there is no proof of the contradiction. > So it is to you to actually *prove* it. > > I did. Consider the sequence T_n of triangles obtained from > arithmetic lists You did not. And now you *again* come with examples rather than a proof. > 1 > 1,2 > 1,2,3 > ... > 1,2,3,...n. > > For every triangle T_n height, diagonal, and base exist. n in N, I presume. > The axiom of > infinity states that in the limit n --> oo height and diagonal > continue to exist (every point of them continues to exist) but the > base does not. The axiom of infinity states nothing about a limit. > This is in clear contradiction with rotational > invariance of geometric figures. But why should it still be a triangle? Consider the situation in Euclidean geometry where triangles are formed by the three points (0, 0), (0, n) and (n, n). These are all triangles. However the figure formed by the line segments (x = 0, y >= 0) and (x = y, x >= 0, y >= 0) do not form a triangle. Or do you think those two line segments form a triangle? If so, what is the base? It is not so in Euclidean geometry that assumes lines of infinite length. > Therefore the axiom of infinity has to be exorcised. Yes, we know that you do not like it. Create a form of mathematics without it, but do not state that it is inconsistent unless you have a proof. > Otherwise, under potential infinity, > I consider only the existing lines. > > I have still not found a definition of potential infinity that is valid > within ZF. > > In ZF everything is valid, because it entails a contradiction, namely > the axiom of actual infinity. Until not not proven. > Axiom Of Potential Infinity: For every natural number there is a set > that contains this number together with all smaller natural numbers, > and for every set of natural numbers there is a natural number that is > larger than every number of the set. > > Briefly: Every set of natural numbers has a largest element. It is > impossible to reasonably talk about all natural numbers. Briefly, you do not want infinite sets. That is, the set of natural numbers does not exist in your vision. > Why? Pick any natural line n. You will see that not omega is the next > one following onto this n but that n + 1 follows --- and that is a > natural number. > > Right. Omega does not follow on a specific natural number. However, I > detect an ambiguity in your statement. Did Cantor really state that > there is a number that follows next on all naturals? > What is the meaning of next on all in that sentence? I would think that > it means there is a smallest number larger than all natural numbers. > You appear to understand it as there is a number that follows some > natural number. I wonder how you come to your interpretation. > > Somit ist beta die auf alle alpha_nu der Gr.9a¤e nach n.8achstfolgende > Ordnungszahl; Ok, so my interpretation was correct. > Eh? This makes no sense. You now explictly state that each number > is followed by a natural number. Can you provide a proof of that > amazing fact? What natural number follows the imaginary number 'i'? > > Please refrain from this nonsene. Of course Cantor and me were talking > about natural numbers. > > You are, Cantor and I are not. Omega is *not* a natural number. I have > stated this before, but apparently you are not able to understand it: > (1) There is no natural number that comes after all natural numbers > (2) There is a number that comes after all natural numbers > These two statements are not in contradiction with each other. > > Cantor does not distinguish between natural and non-natural. See > above. He makes the distinction. He distinguishes finite whole numbers and infinite whole number, putting them in all kinds of classes. The naming in English is a bit different since that time. What is currently defined to be natural numbers were for Cantor the finite whole numbers (now I disremember whether that was class 0 or 1). > ZF has the definition of the axiom of infinity. This claims the actual > existence of all elements of omega. But it is not allowed to pick all > elements of omega together. It is allowed to act only as if omega > would not actually exist but only potentially. > > Eh? Where in ZF do you find that nonsense? If I state N I pick all > elements of N together. This is perfectly allowed by ZF. > > Then you either get a largest or the linearity is lost. Prove it! > If you could use all n simultaneously as you pretend to be able > to in Cantors list, then > E n A m > would be equivalent to > A m E n. > > Why? Can you show a proof? > > All existing means all can be used. > > Makes not sense and is not a proof. E n A m is equivalent to A m E n > only under particular circumstances. You need a proof that it holds > here, because it is not generally true. In general A m E n can be > true while E n A m is not, even if you can consider all n at > simultaneously. The only thing that can be stated is (symbolically): > E n A m P(m, n) -> A m E n P(m, n) > not the reverse, this is just basic logic. (And there are sufficient > finite examples where the reverse does not hold. Or do you think that > you can not simultaneously use a finite number of examples?) > > All these finite (and infinite) examples violate linearity. So you have to prove that it holds under linearity. Because all your attempts until now where based on theorems about finite collections of finite sets or finite collections of finite lines where you do not prove but only wish that what holds for those finite collections also would hold for infinite collections, your proofs failed. See the octant in Euclidean geometry above which, in some sense, can be seen as the limit of a sequence of triangles, but which itself is not a triangle. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Diagonal wanderings (incongruent by construction) What does this mean, I wonder: > ... classical logic was abstracted from the mathematics of finite > sets and their subsets ... > ??? possibly that in finite sets we can decide whether x in S > by a finite numebr of comparisons: x = x1?, x = x2?, ... , x = xn? and so we can find out effectively whether x in S or not x in S; If set membership is all we care about, we then take this as a general > principle of set theory: x in y or not x in y and we have classical logic (the excluded middle being the key > difference between classical and intutionistic logic). Well, this is an attractive argument, but I wonder if classical > logic really was abstracted from arguments of this sort. By classical logic (I forget who the cite is from) was meant, I assume, not the logic of classical (ancient) philosophy, but the logic used by Hilbert and friends in their attempts to provide a foundation for mathematics in particular -- in contrast to Brouwer's intuitionistic logic, for example. At least, that's how I took it, and how the term is usually used in mathemtical logic today. > -- > hz -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) > What does this mean, I wonder: > ... classical logic was abstracted from the mathematics of finite > sets and their subsets ... > ??? > possibly that in finite sets we can decide whether x in S > by a finite numebr of comparisons: x = x1?, x = x2?, ... , x = xn? > and so we can find out effectively whether x in S or not x in S; > If set membership is all we care about, we then take this as a general > principle of set theory: > x in y or not x in y > and we have classical logic (the excluded middle being the key > difference between classical and intutionistic logic). > Well, this is an attractive argument, but I wonder if classical > logic really was abstracted from arguments of this sort. By classical logic (I forget who the cite is from) Weyl. > was meant, I > assume, not the logic of classical (ancient) philosophy, but > the logic used by Hilbert and friends in their attempts to > provide a foundation for mathematics in particular -- I guess we're talking basically, then, about Boole, Frege, Russell and Whitehead, and those others who cleaned up after them (including Hilbert); and maybe Zermelo, if you consider set theory a part of logic. > in contrast to Brouwer's intuitionistic logic, for example. I'm don't think Brouwer really much had a particular logic; I think he felt that mathematics was prior to logic. Nevertheless, he rather grudgingly accepted Heyting's formalization of logic along intuitionist principles (though also calling it a sterile exercise) http://en.wikipedia.org/wiki/Heyting . > At least, that's how I took it, and how the term is usually used > in mathemtical logic today. Ok. The case to be made that the law of excluded middle (LEM) is abstracted from the mathematics of finite sets and their subsets would be hard to make, I think in the case of Russell and Whitehead -- in Principia Mathematical the operation of disjunction is taken as primitive and LEM is proven long before any formalization of class logic is undertaken. I am regrettably ignorant of Frege's work in logic and would not be able to comment on his derivation or justification of LEM. The case of Boole might be more supportive of your thesis. At http://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/CalcLogic.html we read: 1) That the business of Logic is with the relations of classes, and with the modes in which the mind contemplates those relations. (2) That antecedently to our recognition of the existence of propositions, there are laws to which the conception of a class is subject, - laws which are dependent upon the constitution of the intellect, and which determine the character and form of the reasoning process. In Mathematical Analysis of Logic Aristotle's class logic is first analyzed. The same formal system is then interpreted as applied to hypothetical propositions -- what we would call propositional logic. Although the propositional law P v ~P is not thus mathematically *derived* from class logic, it might be held that the consideration of the analoguous class laws underly this interpretation of the calculus. -- hz === Subject: Re: Diagonal wanderings (incongruent by construction) <4A1375B7.358797CE@gmail.com> <4A184470.F90C7C1D@gmail.com> <4A1A3832.11BEACE8@gmail.com> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.10) Gecko/2009042315 Firefox/3.0.10,gzip(gfe),gzip(gfe) > What does this mean, I wonder: > ... classical logic was abstracted from the mathematics of finite > sets and their subsets ... > ??? > possibly that in finite sets we can decide whether x in S > by a finite numebr of comparisons: x = x1?, x = x2?, ... , x = xn? > and so we can find out effectively whether x in S or not x in S; > If set membership is all we care about, we then take this as a general > principle of set theory: > x in y or not x in y > and we have classical logic (the excluded middle being the key > difference between classical and intutionistic logic). > Well, this is an attractive argument, but I wonder if classical > logic really was abstracted from arguments of this sort. > By classical logic (I forget who the cite is from) Weyl. > was meant, I > assume, not the logic of classical (ancient) philosophy, but > the logic used by Hilbert and friends in their attempts to > provide a foundation for mathematics in particular -- I guess we're talking basically, then, about Boole, Frege, Russell > and Whitehead, and those others who cleaned up after them (including > Hilbert); and maybe Zermelo, if you consider set theory a part of logic. > in contrast to Brouwer's intuitionistic logic, for example. I'm don't think Brouwer really much had a particular logic; I think > he felt that mathematics was prior to logic. Nevertheless, he > rather grudgingly accepted Heyting's formalization of logic > along intuitionist principles (though also calling it a > sterile exercise)http://en.wikipedia.org/wiki/Heyting. > At least, that's how I took it, and how the term is usually used > in mathemtical logic today. Ok. The case to be made that the law of excluded middle (LEM) is abstracted > from the mathematics of finite sets and their subsets would be hard > to make, I think in the case of Russell and Whitehead -- in Principia > Mathematical the operation of disjunction is taken as primitive and > LEM is proven long before any formalization of class logic is undertaken. I am regrettably ignorant of Frege's work in logic and would not be > able to comment on his derivation or justification of LEM. The case of Boole might be more supportive of your thesis. Athttp://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/CalcLogic... > we read: 1) That the business of Logic is with the relations of classes, > and with the modes in which the mind contemplates those relations. (2) That antecedently to our recognition of the existence of propositions, > there are laws to which the conception of a class is subject, - laws which > are dependent upon the constitution of the intellect, and which determine the > character and form of the reasoning process. In Mathematical Analysis of Logic Aristotle's class logic is first > analyzed. The same formal system is then interpreted as applied to > hypothetical propositions -- what we would call propositional logic. > Although the propositional law P v ~P is not thus mathematically > *derived* from class logic, it might be held that the consideration > of the analoguous class laws underly this interpretation of the calculus. i think you may be taking the argument from a different direction than it is normally presented the point made by weyl and brouwer (and many others) about the derivation of the law of the excluded middle being improperly abstracted is about operations on finite collections being misunderstood it's not that it actually was formulated this way logic evolved from many different directions with many different analyses of reasoning a common modern example is found in the halting problem it is now known (though certainly wasn't in aristotle's time) that no algorithm can tell us whether arbitrary programs halt in any finite time there are programs that can be proven to halt and those that can be proven to never halt but there are also programs where it will never be determined whether they halt or not no matter how much time elapses so for those philosophies that state truth is an assertion of knowledge or is derived from epistemic verification of obtainment then program X halts can be true false or even something else if the state space of programs were finite the halting problem would always be solvable by simply mapping out the full state graph because the state space is infinite and there is a natural diagonal theorem on it bivalence fails that is the failure of abstraction that is commonly talked about in the finite case there is no need to distinguish epistemic truth from metaphysical assertion so the classical logic often made category errors here (though there is a good tradition of more deliberate analysis going back to the stoic school of logic of before) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Re: Diagonal wanderings (incongruent by construction) Of course, there are non-isomorphic models of > Z set theory, if that's what you mean. > I meant there are *uncountably* many *isomorphic* > models of Q or PA. Nam, you vastly understate your case. Perhaps. Short Usenet dialogs sometimes include understatements, I'd think. Nonetheless my case is genuinely there. > For every > mathematical theory, if there is at least one model, > then there is a proper class of isomorphic models. Agree. For example, for any consistent theory S having the theorem Axy(x=y), there exists a proper class of isomorphic models of S. If this is a problem with PA or Q, then there is > the same problem with all of mathematics. Whatever problem there might with Q or PA, that doesn't necessarily mean, say, the theory S would have that same kind of problem, simply because Q and PA aren't in the same class as S. Q and PA are in the dubious class of formal systems known as as-strong-as-arithmetic, which we could *only assume* we know precisely what that might mean. S isn't in the that class of course! Could you be more specific about what you find > to be a problem with these many isomorphic models > of PA or Q? Specifically, when constructing them, these models can't tell us whether or not the formal systems (Q, PA, e.g.) of the dubious class would be consistent. In a kind of reversed justice formal systems such as Q or PA are created in the image of a particular structure known as the natural numbers, but the formal systems could be syntactically inconsistent! And we've not even mentioned the fact *we have no _precise_ knowledge* out of *uncountably many* existences of 2-ary relations, which one we *could* claim we've picked so that the 2-ary function symbol would stand for. We simply can't! Could you give at least one example of something > you do consider uniquely defined? Sure. I have in my mind there's a unique empty set, denoted by {}, containing no sets at all. The Universe U = {{}} would then comprise a unique model ,say the standard model M, for the formal system say S = {x=y}. There's also a fact that there's a proper class of models of S where any one model M' different from M could be said to be identical to M up-to-isomorphism, as a matter of *informality*. -- To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician. (Shoenfield, Mathematical Logic) === Subject: Re: Diagonal wanderings (incongruent by construction) > Of course, there are non-isomorphic models of > Z set theory, if that's what you mean. > I meant there are *uncountably* many *isomorphic* > models of Q or PA. > Nam, you vastly understate your case. Perhaps. Short Usenet dialogs sometimes include understatements, > I'd think. Nonetheless my case is genuinely there. > For every > mathematical theory, if there is at least one model, > then there is a proper class of isomorphic models. Agree. For example, for any consistent theory S having the > theorem Axy(x=y), there exists a proper class of isomorphic > models of S. > If this is a problem with PA or Q, then there is > the same problem with all of mathematics. Whatever problem there might with Q or PA, that doesn't necessarily > mean, say, the theory S would have that same kind of problem, simply > because Q and PA aren't in the same class as S. Q and PA are in the > dubious class of formal systems known as as-strong-as-arithmetic, > which we could *only assume* we know precisely what that might mean. > S isn't in the that class of course! > Could you be more specific about what you find > to be a problem with these many isomorphic models > of PA or Q? Specifically, when constructing them, these models can't tell us > whether or not the formal systems (Q, PA, e.g.) of the dubious class > would be consistent. In a kind of reversed justice formal systems > such as Q or PA are created in the image of a particular structure > known as the natural numbers, but the formal systems could be > syntactically inconsistent! And we've not even mentioned the fact > *we have no _precise_ knowledge* out of *uncountably many* existences > of 2-ary relations, which one we *could* claim we've picked so that > the 2-ary function symbol would stand for. I meant the 2-ary successor function symbol 'S' We simply can't! > Could you give at least one example of something > you do consider uniquely defined? Sure. I have in my mind there's a unique empty set, denoted by {}, > containing no sets at all. The Universe U = {{}} would then comprise > a unique model ,say the standard model M, for the formal system > say S = {x=y}. There's also a fact that there's a proper class of > models of S where any one model M' different from M could be said > to be identical to M up-to-isomorphism, as a matter of *informality*. > -- To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician. (Shoenfield, Mathematical Logic) === Subject: Re: Diagonal wanderings (incongruent by construction) <4a132c4a$0$297$b45e6eb0@senator-bedfellow.mit.edu> <4a13924d$0$6675$703f8584@textnews.kpn.nl> <4a139b8a$0$6682$703f8584@textnews.kpn.nl> <4a1632a1$0$5423$afc38c87@news.optusnet.com.au> posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > of 2-ary relations, which one we *could* claim we've picked so that > the 2-ary function symbol would stand for. I meant the 2-ary successor function symbol 'S' You can call it a binary relation or you can call it a unary function, but you can't call successor a binary function. Marshall === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > Do you claim the two arguments > if there is no line that contains all other > lines then there exists two lines A and B > such that neither is a subset of the other. > and > two complete lines that share an endpoint > define a triangle > are one and the same argument? Do you claim the two arguments > if there is no line that contains all other > lines then there exists two lines A and B > such that neither is a subset of the other. > and > two complete lines that share an endpoint > define a triangle > are one and the same argument? Both lead to the result We know that both arguments lead to the same > result, This is not the issue. > Please answer the question. Are the arguements > one and the same? What is one and the same? Is 3 the same as 1 + 2? Yes, they are belonging to one and the same proof (that in English is often named an argument) like a non-white surface is required define a white surface. No, they are not one and the same because a non-white surface is not the same as a white surface. What kind of interest do you have in such scholastic word games, arguments/proofs ? I pointed out to you the reason of our divergence. Show me a finite set that obeys [**] but not [*] and I will agree that you are not doing matheology but mathematics. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > Do you claim the two arguments > if there is no line that contains all other > lines then there exists two lines A and B > such that neither is a subset of the other. > and > two complete lines that share an endpoint > define a triangle > are one and the same argument? WM: all my arguments that you qualify different are one and the same. Clearly you apply some meaning to arguments being one and the same. Using this meaning please answer the question. set that obeys [**] but not [*] and I will agree that you are not >doing matheology but mathematics. Recall ii: if all natural numbers and all lines exist The set of all natural numbers is a set of finite numbers that obeys [**] but not [*] - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Do you claim the two arguments > if there is no line that contains all other > lines then there exists two lines A and B > such that neither is a subset of the other. > and > two complete lines that share an endpoint > define a triangle > are one and the same argument? what is meant by one and the same > WM: all my arguments that you qualify different > are one and the same. Clearly you apply some meaning to arguments > being one and the same. Using this meaning > please answer the question. The question was answerered, using this meaning, before you asked. Show me a finite >set that obeys [**] but not [*] and I will agree that you are not >doing matheology but mathematics. Recall ii: if > all natural numbers and all lines exist The set of all natural numbers is a set of finite numbers > that obeys [**] but not [*] That is not of interest. The set of all natural numbers is certainly not a finite set with any set theoretical understanding of being finite. (It is a potentially infinite set = a finite set but not fixed as is required by set theory.) Show me a finite set that obeys [**] but not [*]. You know: Classical logic was obtained from finite sets ... Or explain why you want to change logic when infinite sets are concerned. Or explain why you think that anyone had the right to change logic when infinite sets are concerned. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I After much tooth pulling WM has confirmed that he considers if there is no line that contains all other lines then there exists two lines A and B such that neither is a subset of the other. and two complete lines that share an endpoint define a triangle to be one and the same argument. So, it is silly for WM to claim he is not changing the subject because he is still talking about one and the same argument. If WM wants to change the subject I ask two things. 1. WM should retract his claim to have a proof for ii. 2. WM should state clearly what he now wishes to discuss (In light his interpretation of one and the same, saying that he wishes to discuss one and the same argument is not sufficient.) - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO SV1),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > > Do you claim the two arguments > if there is no line that contains all other > lines then there exists two lines A and B > such that neither is a subset of the other. > and > two complete lines that share an endpoint > define a triangle > are one and the same argument? > Both lead to the result > We know that both arguments lead to the same > result, This is not the issue. > Please answer the question. Are the arguements > one and the same? What is one and the same? Is 3 the same as 1 + 2? > Yes, they are belonging to one and the same proof (that in English is > often named an argument) like a non-white surface is required define a > white surface. > No, they are not one and the same because a non-white surface is not > the same as a white surface. What kind of interest do you have in such scholastic word games, > arguments/proofs ? I pointed out to you the reason of our divergence. Show me a finite > set that obeys [**] but not [*] and I will agree that you are not > doing matheology but mathematics. > 1. [PDF] Cantor's, Godel's, Tarski's, and Turing'sFile Format: PDF/ Adobe Acrobat - View as HTML12 Mar 2009 ... pretations of Cantor's, Godel's, Turing's and Tarski's formal reasoning .... 4.0.18 An elementary proof that P = NP . . . (February 2007) ...alixcomsi.com/ Index01.pdf - Similar pages - 2. P-versus-NP pageAssume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial ... This yields yet another proof that P=NP. The paper is available at ...www.win.tue.nl/~gwoegi/P-versus-NP.htm - 36k - Cached - Similar pages - 3. REDUCTION-AND-TARSKI-S-DEFINITION-OF-LOGICAL-CONSEQUENCEnP (n) is not a logical consequence of P(0), P(1), . . ., P(n), ... are seemingly first-order and Tarski knew that G.9adel had shown first-order proof methods ...biblioteca.universia.net/html bura/ficha/params/id/ 979939.html - 33k - Cached - Similar pages - 4. P = NP problem - Wikipedia, the free encyclopediaA proof of P = NP could have stunning practical consequences, if the proof leads to efficient methods for solving some of the important problems in NP. ...en.wikipedia.org/wiki/ P %3D NP problem - 88k - Cached - Similar pages - 5. 198. On Axiom Systems o f Propositional Calculi. XIII By Shotaro ...and A. Tarski do not give the proof of equivalences. For notations ... 4 r/p, s/q, t/p, u/r *C3 p/Np-5,. CCpCgrCCpqCpr. 5 r/p, q/Cqp *C3 q/Cqp- C3-6, ...joi.jlc.jst.go.jp/JST.Journalarchive/pjab1945/41.904? from=Google - MM === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > I have still not found a definition of potential infinity that is valid > within ZF. > The definition of potential infinity would avoid that obvious > contradiction. I do not know whether it would make ZF free of > contradictions. But that is not my concern. I need that axiom only for > arithmetics where the natural numbers already are known. More precisely, I don't need any axiom at all. Natural numbers are there whether or not someone takes the trouble to formalize them. But it will help you (Dik) to understand potential infinity. Once again, this thread is quickly approaching that thousand post > mark yet again, which means that Google users such as WM and > myself will be leaving the thread soon. So it is. I noticed how earlier, a standard set theorist (I forgot which one) > made a crack about how since WM is an ultrafinitist and Google's > maximum thread length is a thousand, This is so since the thread A consideration concerning the diagonal argument of G. Cantor, started by albrecht here in sci.logic in Jan. reached 9244 posts in Oct. 2008. > this means WM must > believe that 1001 is the largest number. Debates about Google and > other ways to access Usenet aside, I doubt that there's a link > between ultrafinitism and Google use. (Phil Carmody might have > found a link between being a so-called crank/idiot and Google, > but not all cranks are ultrafinitists. In particular, I'm not an > ultrafinitist -- I freely admit that the number 1002 exists, and WM's > upper bound far exceeds this number.) Please note: There is no upper bound. There is no largest natural number. Since I'll be leaving the thread soon, let me at least comment on > WM's latest attempt to work with Potential Infinity: > Axiom Of Potential Infinity: For every natural number there is a set > that contains this number together with all smaller natural numbers, > and for every set of natural numbers there is a natural number that is > larger than every number of the set. I see nothing wrong with this axiom, or trying to replace the usual > Axiom of Infinity (which WM calls the Axiom of _Actual_ Infinity in > order to distinguish it from his new axiom) of ZF with this axiom, to > obtain the new theory ZF-(Actual) Infinity+WM's Potential Infinity. It > has no affect on the Axiom of Extensionality, unlike WM's previous > attempts to define Potential Infinity, so the standard set theorists > can't use Extensionality as an excuse to ignore this axiom. We might even try to write the axiom in the language of ZF. We try: AneN (Ex (AmeN (m<=n -> mex))) & Ay (EneN (AmeN (mey -> m exist in WM's theory, so how can we even mention N in this axiom, > when we can only talk about that which _exists_? N exists just as a potentially infinite set, AneN means for all natural numbers that you can think of, specify, name, identify, write, ... briefly: For all that are there. Perhaps, instead of a set N, we can define the one-place predicate > N(x), intended to agree with the standard definition of natural number > (so that N(x) <-> x is a natural number). Then the axiom becomes: An (N(n) -> Ex (Am ((N(m) & m<=n) -> mex))) & Ay (En (N(n) & Am ((N(m) > & mey) -> m replace the word natural with ordinal, then the resulting > formula is actually a theorem of ZF, and serves as a definition > of successor and limit ordinals.) Is it? For every set of ordinals, there is an ordinal larger than the ordinals of that set. This means that you can pick every set of ordinals. Doesn't it imply the existence of the set of all ordinals? Or do you presuppose that you can pick every set of ordinals because the set of all ordinals is anyhow excluded? However: If so, then you see that set theory does not improve the situation. In potential infinity the set N is never understood as a set that cannot be increased. In set theory, N is a set that cannot be increased, but on the next level the set of all ordinals, as a set that cannot be increased, must be excluded. This always reminds me on the problem of initial creation. The world could not create itself. So God is introduced. But the question who created God is forbidden. If we use the complete set N (that cannot be increased by any element), then we are forced to introduce larger ordinals. But then we are not allowed to use the set of all these ordinals. So we haven't won anything but have left the solid grounds of science and have invented a highly questionable hypothesis. That is why I find that mathematics has evolved to what better would be called matheology. === Subject: Re: Diagonal wanderings (incongruent by construction) Nntp-Posting-Host: hera.cwi.nl > I have still not found a definition of potential infinity that is > valid within ZF. > The definition of potential infinity would avoid that obvious > contradiction. I do not know whether it would make ZF free of > contradictions. But that is not my concern. I need that axiom only for > arithmetics where the natural numbers already are known. > > More precisely, I don't need any axiom at all. Natural numbers are > there whether or not someone takes the trouble to formalize them. > But it will help you (Dik) to understand potential infinity. Note Lwalker: WM does not want axioms. He only wants intuititions and is not willing to formalise mathematics. > Once again, this thread is quickly approaching that thousand post > mark yet again, which means that Google users such as WM and > myself will be leaving the thread soon. > > So it is. So everybody should allow for users of badly designed software? Pray keep in mind that I have no idea (and no way to easily get the figure) ISP's where you can read news without the recent Google trick to snip > Axiom Of Potential Infinity: For every natural number there is a set > that contains this number together with all smaller natural numbers, > and for every set of natural numbers there is a natural number that is > larger than every number of the set. > > I see nothing wrong with this axiom, or trying to replace the usual > Axiom of Infinity (which WM calls the Axiom of _Actual_ Infinity in > order to distinguish it from his new axiom) of ZF with this axiom, to > obtain the new theory ZF-(Actual) Infinity+WM's Potential Infinity. It > has no affect on the Axiom of Extensionality, unlike WM's previous > attempts to define Potential Infinity, so the standard set theorists > can't use Extensionality as an excuse to ignore this axiom. > > We might even try to write the axiom in the language of ZF. We try: > > AneN (Ex (AmeN (m<=n -> mex))) & Ay (EneN (AmeN (mey -> m > But there's one problem -- the set N, of course, is not supposed to > exist in WM's theory, so how can we even mention N in this axiom, > when we can only talk about that which _exists_? > > N exists just as a potentially infinite set, AneN means for all > natural numbers that you can think of, specify, name, identify, > write, ... briefly: For all that are there. Meaning it can not be written formally. Again: WM does not like formal axioms. > If we use the complete set N (that cannot be increased by any > element), then we are forced to introduce larger ordinals. But then we > are not allowed to use the set of all these ordinals. What axiom of ZF does allow the set of all ordinals? -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Alan Schwartz Jewish science in full-bloom I apologise and will no longer read or contribute to the debate. My only excuse is that I unfortunately came across Potter's anti- > semitism when he cross-posted to a group in which I participate: > racing cycling of all things. I was so morally outraged and indignant > that I followed him across Usenet: it is slightly hypocritical of me > to then continue to post in groups whose members feel the same as I > did back then. Ignoring him is probably best. Probably so. -- hz === Subject: int uv <= int u posting-account=jXDJAgoAAACvCBNKtFyPLZBPxKdTyO2v .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) 1.0 localhost.localdomain:8080 (squid/2.6.STABLE5) Let u and v coninuous on [0,1]. u decreases on [0,1] v takes its values in [0,1]. Let a=int(v(x), x=0..1) Proof that int(u(x)*v(x), x=0..1) <= int(u(x), x=0..a) thank you for advance. === Subject: Re: int uv <= int u Let u and v coninuous on [0,1]. u decreases on [0,1] > v takes its values in [0,1]. Let a=int(v(x), x=0..1) Proof that int(u(x)*v(x), x=0..1) <= int(u(x), > x=0..a) thank you for advance. Hint: Consider the functions F(x) = int_{t=0}^{x} u(t)*v(t) dt G(x) = int_{t=0}^{int_{t'=0}^{x} v(t') dt') u(t) dt. and compare F'(x) and G'(x). Best wishes Torsten. === Subject: Re: Random modular arithmetic question posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.10) Gecko/2009042315 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Hi all While following the latest round of JSH's Pell's equation ranting, it > occurred to me to wonder whether there are Diophantine equations for > which no solutions exist, but which can be solved mod N for every > positive natural number N. Can somebody give me an example, together > with a proof that it is such? (I have a vague recollection that > somebody said that there exist integers which are perfect cubes mod N > for every N but which are not perfect cubes, for example.) achava as always has given a good intro into the theory but i'm surprised no one has mentioned the keywords hasse's principle or the local-global principle there is a great literature on the concept which is usually introduced in the theory of elliptic curves or general diophantine equations beyond quadratics anyway the keywords will help you find more info -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Re: Random modular arithmetic question posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) On 21 May, 19:32, Robert Israel While following the latest round of JSH's Pell's equation ranting, it > occurred to me to wonder whether there are Diophantine equations for > which no solutions exist, but which can be solved mod N for every > positive natural number N. Can somebody give me an example, together > with a proof that it is such? (I have a vague recollection that > somebody said that there exist integers which are perfect cubes mod N > for every N but which are not perfect cubes, for example.) w^2 + x^2 + y^2 + z^2 + 1 = 0 Hint: Lagrange's four-square theorem. === Subject: Re: Random modular arithmetic question posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt MathPlayer 2.10d; .NET CLR 1.1.4322; PeoplePal 3.0),gzip(gfe),gzip(gfe) > On 21 May, 19:32, Robert Israel While following the latest round of JSH's Pell's equation ranting, it > occurred to me to wonder whether there are Diophantine equations for > which no solutions exist, but which can be solved mod N for every > positive natural number N. Can somebody give me an example, together > with a proof that it is such? (I have a vague recollection that > somebody said that there exist integers which are perfect cubes mod N > for every N but which are not perfect cubes, for example.) > w^2 + x^2 + y^2 + z^2 + 1 = 0 > Hint: Lagrange's four-square theorem. > I didn't make it into work yesterday, but I did today, so here is the reference to my comments about Cyclotomic polynomials: On the Reducibility of Cyclotomic Polynomials over Finite Fields by Brett A. Harrison in the American Mathematical Monthly November 2007, not quite as recent as I thought. In it he includes the following goodies: 1) R. Brandl showed in the 1986 Monthly that there is a polynomial of degree n that is irreducible over the integers yet reducible modulo all primes if and only if n is composite. 2) S. W. Golomb showed in the 1978 Monthly that the cyclotomic polynomial of order n, all of which are irreducible over the integers, are reducible modulo all primes if and only if n is not of the form 1, 2, 3, p^k, 2p^k for all odd primes p. Note that this leaves a lot of cyclotomic polynomials which are reducible modulo all primes p. 3) Brett Harrison showed that cyclotomic polynomials are reducible modulo all primes p if and only if the discriminant of the polynomial is a square. Density Theorem which looks like a pretty cool theorem to me. It also lists Mr. Harrison as being associated with a high school. I expect it is a fairly unusual high school math teacher who knows the subject at this level. Achava === Subject: Re: Differential form of a Lorentz transformation posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I'm reading a paper which has the usual Lorentz transformation for > time between S and S' moving with velocity v: t = Y(t' + Bx'/c), with Y = 1/ sqrt(1 - B^2), B = v / C. The author then situates a clock at x' = 0 and says the differential > form of the above for B = B(t) is: dt' = [ 1/Y(t) - t/Y(t)^2 d/dtY(t) ] dt with Y(t) = 1/ sqrt(1 - B(t) > ^2) It really does not matter how one takes the Lorentz transform into the next step where B is dependent on t. That is because you can still write a concise equation by squaring the temporal term and subtracting the sum of the squared of the spatial terms. The Lorentz transform leads to the following spacetime first noticed by Minkowski. B, then, disappears from the mathematics. c^2 dt'2 [CapitalEth] dx'^2 [CapitalEth] dy'^2 [CapitalEth] dz'^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 Or ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 Or c^2 dTau^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 Where ** ds^2 = c^2 dt'2 [CapitalEth] dx'^2 [CapitalEth] dy'^2 [CapitalEth] dz'^2 ** dTau^2 = ds^2 / c^2 = Proper time squared The self-styled physicists aka Einstein Dingleberries have tried to promote mysticism through what proper time actually is. Apparently, the zombie-brained mass who insist on seeing the naked emperor having clothes on cannot offer any honorable objections because of peer pressure or just ones' stupidity. === Subject: Computing the SVD of a matrix from its submatrices !!! posting-account=jYQqJgoAAAD8kGJ-fk0xVxC3e40Qeh85 SLCC1; .NET CLR 2.0.50727; InfoPath.2; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) Hello everybody, I want to develop an algorithm to compute the Singular Value Decomposition (SVD) for a matrix using its sub-matrices: Specifically, 1) Suppose that I have a matrix A which I want to split into two submatrices say B and C in a way that , for example, B contains the 4th, 5th, 16th and 17th raws of A, and C contains the remaining raws. 2) I want to apply some operations on B and C (like the SVD) and then combine the solution somehow to get the SVD of the original matrix A without applying the SVD on the original matrix A itself... Cindy. === Subject: Re: Axiom of Truth > Axiom of Truth: The Axiom of Truth states no infinite set is > prohibited from being called countable providing the set is able to > be referred to explicitly or by symbolic reference.All numbers are > countable. The only restrictions of countability refer to time. > You are posting in the wrong newsgroup as such vagueness are, to give it an undue complement, junk philosophy. Stop replying to others with comments that have nothing to do with the point of discussion being considered. Stop butting into others' discussion with your absurd ego touting claims. They have been refuted more than once. So grow up and get ever it, fame isn't for free. On the other hand if you continue to reply to others with your non-sequitur boastings, I'll black list you and never again will any of your posts ever be down loaded for me to read. Beware, others are getting fed up with you and may also black list you. === === Subject: Re: wavelength/Diameter question- Resolving power is equal to theta = wavelength (of light) / diameter > (of aperture) of a telescope. How is the relationship acquired? I know there is a sine involved.. as in sine theta = wavelength / diameter but what has the wavelength (of light) got to do with the > diameter (of the aperture) geometrically? For example, wavelength at green light is 0.00055 micron > Aperture is say 100mm. Resolving power is theta = 0.00055/100 = 0.0000055 radian > or 1.34 arcsecond How does wavelength, diameter relate geometrically? Why? > Pete See Wikipedia: http://en.wikipedia.org/wiki/Diffraction_formalism and http://en.wikipedia.org/wiki/Diffraction and any textbook on physical optics. The picture at http://en.wikipedia.org/wiki/File:TwoSlitInterference.svg says it all! The same diffraction principle is applied in practical radio astronomy, specifically in arrays of radio telescopes. See for instance http://en.wikipedia.org/wiki/Radio_astronomy and http://en.wikipedia.org/wiki/Lofar . Ciao: Johan E. Mebius === Subject: Has Larry Sarner Been Defeated by Mathematics? posting-account=A2rtMwoAAACiQZRb17VN8BH3JZMlCZXL Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) Larry Sarner - where to begin? The man waxes eloquent on many topics-topics he knows nothing about. He seems to have made it his life's work to criticize and condemn those whose life's work is helping orphans and other children with problems. Larry Sarner is a god with feet of clay. Larry Sarner is a man with feats of a less pleasant substance. a doctor. Sarner has never treated a patient. Words like ïquackery' and ïpseudoscience' are often associated with Larry Sarner, and with good reason. Sarner cannot design and execute a double blind experiment. Sarner practices hate propaganda techniques reminiscent of the Church of Scientology. Is it possible he shares Scientology founder L. Ron Hubbard's bizarre ideas on mathematics and the scientific method? Hubbard's hilarious essay on calculus could be the model for some of Sarner's saner rants. Just to be clear-Sarner is not a debunker or quackery or pseudoscience, so one need not ascribe the accolades of James Randi to him. Sarner is, rather, a practitioner of quackery and pseudoscience, and, sadly not a very entertaining one at that! Would you like to know more about Larry Sarner? Start here.83 http://larrysarnerpseudoscience.wordpress.com/2009/05/07/where-did-larry-sar ner-learn-mathematics/ http://larrysarnerpseudoscience.wordpress.com/2009/04/30/larry-sarner-fails- at-experimental-design/ http://medicalcrackpots.wordpress.com/2009/05/09/larry-sarner/ === Subject: Re: Ooops... An Inertial Motion Detector posting-account=wigfZgkAAACDgITarXffzxJygX81YRSs Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) story of cherries .... i read also the other things , but the cherries > pickup by me , are intouched ... inside a rocket started at 200.000 > km.s.from your garden , do you think possible send a bullet in the > same direction at 200.000 km.s.? Of course it is. are p + p, d + Au, Cu + Cu and Au + Au. The projectiles > typically travel at a speed of 99.995% of the speed of > light in vacuum. For Au + Au collision, the center-of-mass > energy sqrt{s {NN}} is typically 200 GeV (or 100 GeV per nucleus); http://en.wikipedia.org/wiki/Relativistic Heavy Ion Collider smiles and frish cherries.. :-) Sue... ...and from the window of rocket ,somebody could see inside 1)a > bullet going at 400.000 km.s. or 2)a bullet with very high > energy ? ..you can choose and confront with the consequences ...note > that my dog , inside the rocket , think rightly to be in aninertial > frame ( sistem ).. What people see is not the result of Newton's > of the gravito-inertialfield so it bears little > consideration. A very massive bullet, passing would be necessary > to get your dog scratching his head about anomalous > results. > http://www.bestweekever.tv/bwe/images/2007/12/9%20dog%20professor.JPG << Einstein's relativity principle states that: Allinertialframes are totally equivalent > for the performance of all physical experiments.> http://farside.ph.utexas.edu/teaching/em/lectures/node108.html Sue... itself too much ..one easier example(another!) : i convinced my dog to > start with a rocket at 200.000km.s. and i too start with same speed in > opposite direction ...: after 10 sec. , which distance it is between > me and my dog ? For modern time dependent Maxwell's equations and > no Cherenkov radiation: 200.000km/s x 10sec x 2paths = 4.000.000km > http://whyslopes.com/etc/fractions/fractions18a constant speed and ve... > http://espg.sr.unh.edu/ism/what1.html http://en.wikipedia.org/wiki/Free space :-) To assume Newton's light-corpuscle moving under the > influence of inertia, some problems are attendant > that can be approximately resolved with some > smearing and curve-fitting: << Can we construct a new transformation which makes > the velocity of light invariant between differentinertialframes, in accordance with the relativity > principle, but reduces to the Galilean transformation > at low velocities, in accordance with our everyday > experience? > http://farside.ph.utexas.edu/teaching/em/lectures/node110.html You should note that *light* in that page assumes > equations used. < or with modern terminology, photons, were > explicitly mentioned in the reports on which > the prize decision rested only in connection > with emission and absorption processes. The > Committee says that the most important application > of Einstein's photoelectric law and also its most > convincing confirmation has come from the use > Bohr made of it in his theory of atoms, which Sue... ...so i am departing from my dog at 400.000 km.s . . . . ( perheps you > can say that in some different way ..) Suddenly i remember that > my dog started without foods and immediately i shoot a flesh' torpedo > in direction of my dog at 500.000km.s.....: i am sure that my dog > shall not die famished ! ( Einstein permitting ?) and Sue ... > permitting ? An uncharged doggy treat just barely gets off your ship with present technology. << Neutrons from fusion reactions are usually considerably more energetic than 1 MeV; the produces 14.1 MeV neutrons (1400 TJ/kg, moving at 52,000 km/s, 17.3% of the speed of light) that can easily fission uranium-238 and other non-fissile actinides. > http://en.wikipedia.org/wiki/Fast neutron Let us say your dog will eat heavy ions. Then you could have the a silver atom exit the rear of your ship at nearly 300.000km/sec wrt the ship. The electrical charge that the accelerator used to grip the ion is about 10^32 times greater that the gravito-inertial force which you expect will pull the ion toward your dog. http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/elefor.html#c2 It's trajectory will be more like charged we shoot when bird hunting. http://www.sunearthplan.net/3/interplanetary-space http://en.wikipedia.org/wiki/Lorentz force I hope your dog carries a little extra fat. :-( Sue... === Subject: Re: Ooops... An Inertial Motion Detector posting-account=XbpThQoAAACtPo22j_KAb5B7K8_euNJy Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) you was enough convincent ..and also we cannot continue that experiment : my dog is completely unreliable ( he took a cheese ' piece and simulated the starting ..bahh )... i invite you on the other table '' wave model ..ligth..einsteniana'' === Subject: Re: Ooops... An Inertial Motion Detector posting-account=wigfZgkAAACDgITarXffzxJygX81YRSs Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) you was enough convincent With apologies to Richard Fiztpatrick, the substance of the argument is not mine. It is simply the result of getting a few cobwebs out of the attic and updating some concepts so they conform with modern experience. << A book based on these lectures notes, entitled Maxwell's Equations and the Principles of Electromagnetism, is now available from Infinity Science Press, Hingham, MA. (ISBN: 978-1-934015-20-9) > http://farside.ph.utexas.edu/teaching/em/em.html > ..and also we cannot continue that > experiment : my dog is completely unreliable ( he took a cheese ' > piece and simulated the starting ..bahh )... i invite you on the other > table '' wave model ..ligth..einsteniana'' is not very good. It is just better than any of the other languages I have tried to write. There are a few colourful variations used in this forum that don't seem to correlate with academic papers but I have a sailor friend that helps me with the translation. ;-) When I become proficient enough with English to use it as an effective communication tool, I might try some of the other languages I see on your very interesting forum. Sue... === Subject: Re: What happens to your shape when you move into curved space? <6e877$4a044407$cdd0850a$1164@DIALUPUSA.NET> posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > If you occupy a curved geometry you will share its shape. Matter and > light extend in curved space. Mitch Raemsch Your brain exists in the 4th dimension of curved > space, thus being inaccessible to you. We extend in the round 4th dimension's surface. Mitch Raemsch === Subject: Re: The complete infinite binary tree has only countably many infinite paths. > 0.333... is an abbreviation of 1/3 or one third, exactly. > But 0.333... is only a name consisting of eight symbols. > By means of digits it seems impossible to get more than the sequence > (a_n) = SUM [n in N] 3*10^-n > 0.3 > 0.33 > 0.333 > ... > which does not include a representation of 1/3 with an infinite number > of digits. I conclude that it is not possible to obtain such a > representation. Do you know a tool how to accomplish it? > Perhaps something other than a list of finite-length digit strings? Namely? Um, something that produces infinite-length digit strings? 0.333... is a digit string of infinite length. Your attempt > to construct it using a sequence of finite-length digit > strings is obviously the wrong approach. It's like trying > to find an odd number by listing all the even numbers. > It simply, and obviously, does not work. Perhaps you should consider a method that produces > strings of infinite length in order to derive the particular > string you're looking for Such a method does not exist. At least it does not appear in any > Cantor list. Such lists as Cantor shows to be incomplete are not restricted to any method of generation. > If it would exist, then the binary tree would show that the number of > reals is limited by a countable set. On the contrary, if one proves that no countable list suffices, as Cantor has done quite successfully, then the number of binary strings is not countable, and it inevitably and easily follows that the number of reals in any interval of positive length is also not countable. That WM has no effective grasp of the reals also follows. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. Every line is constructable. > Everything that does exist is constructable. Even in strict constructivism that is not claimed. The most that is > claimed is that unless a thing can be constructed it cannot be KNOWN to > exist. If these things are nothing but thoughts, then cannot be known to > exist is tantamount to exist. They are also not known not to exist, so WM, as usual, tries to beg the question.. Your kind of maths requires that you deny the basic equality > every element and all smaller elements = all elements. Is that one of the axioms of WM's anti-set theory? > It is certainly not true for elements which are not ordered. > And the mention of elements presumes a set to which they belong. every element and all smaller elements = all elements But nothing is an element unless there is set of which it is an element, as element means nothing more than member of a set.. > This is an axiom that holds for all sequences, for instance the > sequence of natural numbers. And for which there are no all elements unless one has a set of all naturals of which they are elemetns. > If you find a theory which does not accept this axiom, then better > forget it. By my axioms, anything that is an element is an element of a set, and any reference to all elements presupposes the set to which they all belong. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Every line is constructable. > Everything that does exist is constructable. Even in strict constructivism that is not claimed. The most that is > claimed is that unless a thing can be constructed it cannot be KNOWN to > exist. If these things are nothing but thoughts, then cannot be known to > exist is tantamount to exist. They are also not known not to exist, so WM, as usual, tries to beg the > question.. > Of course I meant: cannot be known to exist is tantamount to do not exist. Your kind of maths requires that you deny the basic equality > every element and all smaller elements = all elements. Is that one of the axioms of WM's anti-set theory? > It is certainly not true for elements which are not ordered. > And the mention of elements presumes a set to which they belong. every element and all smaller elements = all elements But nothing is an element unless there is set of which it is an > element, as element means nothing more than member of a set.. Then denote the elements by term or simply by natural number. I am interested in the natural numbers, not in the set of natural numbers (if this set is a different thing from all natural numbers). This is an axiom that holds for all sequences, for instance the > sequence of natural numbers. And for which there are no all elements unless one has a set of all > naturals of which they are elemetns. That does *not* make a difference, unless the set N is *more* than all natural numbers which I can consider even without considering a set. But in general you deny that that N is more. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. > Every line is constructable. > Everything that does exist is constructable. Even in strict constructivism that is not claimed. The most that is > claimed is that unless a thing can be constructed it cannot be KNOWN to > exist. If these things are nothing but thoughts, then cannot be known to > exist is tantamount to exist. Does WM claim that I cannot think of a set of all naturals? That such a thought, even when its existence is evidenced by more than half of the posts in this thread, cannot occur? Maybe in WM's world, but elsewhere it is only those things which can be known not to exist which can be known not to exist, and even they can be thought of, and the set of naturals is not such a thing. They are also not known not to exist, so WM, as usual, tries to beg the > question.. Of course I meant: > cannot be known to exist is tantamount to do not exist. That is an assumption that most of us find unwarranted and, at least in mathematics, sometimes necessarily false. Your kind of maths requires that you deny the basic equality > every element and all smaller elements = all elements. Is that one of the axioms of WM's anti-set theory? > It is certainly not true for elements which are not ordered. > And the mention of elements presumes a set to which they belong. every element and all smaller elements = all elements But nothing is an element unless there is set of which it is an > element, as element means nothing more than member of a set.. Then denote the elements by term or simply by natural number. > I am interested in the natural numbers, not in the set of natural > numbers (if this set is a different thing from all natural numbers). If all natural numbers is a thing, it is so like a set as to be indistinguishable from one. This is an axiom that holds for all sequences, for instance the > sequence of natural numbers. And for which there are no all elements unless one has a set of all > naturals of which they are elements. That does *not* make a difference, unless the set N is *more* than > all natural numbers It is somewhat different from all natural numbers as being a singleton which all natural numbers is patently not. But if all natural numbers is allowable, then only the most perverse of logic denies the set of them. which I can consider even without considering a > set. But in general you deny that that N is more. Different, but only more in the sense of being a sort of logical boundary between natural numbers and other things. numbers. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > If these things are nothing but thoughts, then cannot be known to > exist is tantamount to cannot exist. Does WM claim that I cannot think of a set of all naturals? That such a > thought, even when its existence is evidenced by more than half of the > posts in this thread, cannot occur? A thing that exists only as a thought and that cannot be thought does not exist. But if a thing can be thought of this doe snot imply that the thing exists. It is a necessary condition for thought things that they can be thought of. It is not a sufficient condition. They are also not known not to exist, so WM, as usual, tries to beg the > question.. Of course I meant: > cannot be known to exist is tantamount to do not exist. That is an assumption that most of us find unwarranted and, That is not an assumption but the definition of a thing that exists only as a thought. A thing that exists only as a thought and that cannot be thought does not exist. at least in > mathematics, sometimes necessarily false. Not in mathematics but in matheology where you assume the xistence of numbers, i.e., thought things, that cannot be thought of as individuals. That's why I call this kind of superstition matheology. This was my last contribution to this thread. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. If these things are nothing but thoughts, then cannot be known to > exist is tantamount to cannot exist. Does WM claim that I cannot think of a set of all naturals? That such a > thought, even when its existence is evidenced by more than half of the > posts in this thread, cannot occur? A thing that exists only as a thought and that cannot be thought does > not exist. That does not apply to the set of naturals which clearly can be a thought and has been for a long time. > But if a thing can be thought of this doe snot imply that the thing > exists. No natural exists as other than s a thought, or a record of something thought. It is a necessary condition for thought things that they can be > thought of. It is not a sufficient condition. Then no numbers can exist, only oral or written records of their being thought of. While WM can easily write down or point to a numeral (name of a number), They are also not known not to exist, so WM, as usual, tries to beg the > question.. Of course I meant: > cannot be known to exist is tantamount to do not exist. That is an assumption that most of us find unwarranted and, That is not an assumption but the definition of a thing that exists > only as a thought. It is not a definition of anything for those not encapsulated within WM's world of MathUnrealism. > A thing that exists only as a thought and that cannot be thought does > not exist. But I, at least, can think of N, so your stricture fails. at least in > mathematics, sometimes necessarily false. Not in mathematics but in matheology where you assume the xistence of > numbers, i.e., thought things, that cannot be thought of as > individuals. Who says that they can't be thought of as individuals? There must be some sort of a hitch in the giddyup of WM's thinker. That's why I call this kind of superstition matheology. This was my last contribution to this thread. Promises, promises !!! === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > However, for every natural number, there is a line that contains it. That's what I meant. All natural numbers are elements of the union of > all lines. This is true. This is not true, but merely a meaningless sentence. But it would be > true if all natural numbers and all lines existed. So we have WM: if > all natural numbers and all lines exist > then > all natural numbers are elements of the union of > all lines. from which immediately follows i: if > all natural numbers and all lines exist > then > no line contains all natural numbers This is the first half of the putative contradiction. To finish this contradicton we need ii: if > all natural numbers and all lines exist > then > there exists a line that contains all natural numbers However, if all natural numbers exist and all lines exist, > then neither the set of natuaral numbers nor > the set of lines has a last element. > To finsh the contradiction, we need a proof of ii > that does not assume a last element. Every line contains all numbers that are in the preceding lines. If all numbers exist, then they exist in one line. This is proved by induction over all the finite initial segments of the set of lines. Your logic is what fails. I will leave this thread because in near future it will explode. You know there is another one with related topic. There it has been shown: You can reach every natural number by a Turing machine. Nevertheless, in every case, there are infinitely many numbers remaining. That means: every and all smaller is different from all. As long as you insist on this falsity, further discussion is useless. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > However, for every natural number, there is a line that contains it. That's what I meant. All natural numbers are elements of the union of > all lines. This is true. This is not true, but merely a meaningless sentence. But it would be > true if all natural numbers and all lines existed. So we have WM: if > all natural numbers and all lines exist > then > all natural numbers are elements of the union of > all lines. from which immediately follows i: if > all natural numbers and all lines exist > then > no line contains all natural numbers This is the first half of the putative contradiction. To finish this contradicton we need ii: if > all natural numbers and all lines exist > then > there exists a line that contains all natural numbers However, if all natural numbers exist and all lines exist, > then neither the set of natuaral numbers nor > the set of lines has a last element. > To finsh the contradiction, we need a proof of ii > that does not assume a last element. (As requested I am continuing this in another thread) - William Hughes === Subject: Re: The complete infinite binary tree has only countably many infinite paths. > However, if all natural numbers exist and all lines exist, > then neither the set of natuaral numbers nor > the set of lines has a last element. > To finsh the contradiction, we need a proof of ii > that does not assume a last element. Every line contains all numbers that are in the preceding lines. True but irrelevant. It is the fact that however long a line of naturals one deletes, there are as many naturals undeleted as exist. > If all numbers exist, then they exist in one line. WM is blind to the painfully obvious fact that it is only if NOT all naturals exist that one can squeeze all that do exist into one line. > This is proved by > induction over all the finite initial segments of the set of lines. Wm claims such a proof but never produces it. Such claims without proof are mere to air. Your logic is what fails. It only fails to penetrate the density of WM's stupidity, but to penetrate such stupidity, the gods themselves strive in vain. > I will leave this thread because in near future it will explode. And then all of WM's false claims in it will vanish in the wind and never be heard of again. === Subject: Re: Mental Event & Mental Object: Is there a Difference? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) What's a 'mental state'? A part of your nature, therefore a part of your identity, why would you want to deny that, if not because you dont want to be held responsible for what comes from it? MG === Subject: Re: Mental Event & Mental Object: Is there a Difference? > What's a 'mental s spin, crudophile === Subject: Re: Mental Event & Mental Object: Is there a Difference? posting-account=qKxGxgkAAADAPfYVCc-ZQkIzl0senr2M .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 1.1.4322; Zune 2.5),gzip(gfe),gzip(gfe) (snip sophistry) Q: Mental Event & Mental Object: Is there a Difference? A: If you think so. Tom Davidson Richmond, VA === Subject: Re: Mental Event & Mental Object: Is there a Difference? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) Q: Mental Event & Mental Object: Is there a Difference? A mental event without a material object and or its nature, giving rise to that mental event - results in man going to church, slamming jets into sky-scrapers, ing little boys in church, being dopey brain dead Kantians, being an anti-human masochistical sadistical parasitical socialist and of course it was a mental event without a material object giving rise to the mental event, that resulted in your silly matterless mental event Kantian question. MG === Subject: Re: Mental Event & Mental Object: Is there a Difference? Q: Mental Event & Mental Object: Is there a Difference? A mental event without a material object and or its nature, giving > rise to that mental event - results in man going to church, slamming > jets into sky-scrapers, ing little boys in church, being dopey > brain dead Kantians, being an anti-human masochistical sadistical > parasitical socialist and of course it was a mental event without a > material object giving rise to the mental event, that resulted in your > silly matterless mental event Kantian question. I wish I had lived before Kant had been born, when people didn't do terrible things. Damn. -- hz === Subject: Re: Mental Event & Mental Object: Is there a Difference? <4A064F28.4B49836E@gmail.com> posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > I wish................ How very Kantian MG === Subject: Re: Mental Event & Mental Object: Is there a Difference? I wish................ How very Kantian If only I had been born before Kant lived, when people didn't make wishes, or consider hypothetical propositions. Life was simpler then. -- hz === Subject: Re: Mental Event & Mental Object: Is there a Difference? <4A066F26.A7B73E83@gmail.com> posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) If only............. How very Kantian! Try begining with - *It is......* you know, something you can be certain about which will scare the living out of any Kantian. MG === Subject: Re: Mental Event & Mental Object: Is there a Difference? posting-account=hA77jwoAAABvWF820QwAlfYdLdF7G8UH Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Yes, a 'mental state' is an object. > It is not an object. Mr. Jones, anything one observes of a state is a > tentative declaration of something within its moment. It is not that > moment, nor what it was (to you or any observer) at that moment. > Jones - your object is DEAD. > A mental state is an object, and because it is an object it is an > example of bad grammar. So your position is the same as mine. A mental state is only an object to a machine or to another person. > Your own mental state is a subject. Your statement is an abuse of > language. What's a 'mental state'? What's 'my own mental state'? > Why give this mental term a false credence by treating it as a physical > object? I am not saying it is an object. Why not READ what I said? You can only make an object of the mental state of another. Your mental state is a subject and subject to that to which is referred. === Subject: Re: Mental Event & Mental Object: Is there a Difference? > Yes, a 'mental state' is an object. > It is not an object. Mr. Jones, anything one observes of a state is a > tentative declaration of something within its moment. It is not that > moment, nor what it was (to you or any observer) at that moment. > Jones - your object is DEAD. > A mental state is an object, and because it is an object it is an > example of bad grammar. So your position is the same as mine. > A mental state is only an object to a machine or to another person. > Your own mental state is a subject. Your statement is an abuse of > language. > What's a 'mental state'? What's 'my own mental state'? > Why give this mental term a false credence by treating it as a physical > object? I am not saying it is an object. Why not READ what I said? You can > only make an object of the mental state of another. Your mental state > is a subject and subject to that to which is referred. I know you say 'it' or the mental state is a subject, but you are phrasing it like it's an object. === Subject: Re: -- Packing unit circles in tans: new results In this post, new packings for N = 30 and 58 are given, inserted in numerical order among the previous ones. > Packomania has, very recently, added a new section about packing > circles in tans, i.e., isosceles right triangles: > This thread will give some improvements, attempting to pack N unit > circles in the smallest possible tan. In my figures, tangencies are indicated by a small normal segment, and > circles are color-coded according to their number of tangencies: red, 0; > purple, 3; green, 4; yellow, 5; orange, 6. For each packing, the > leg length s of the tan is given; this value corresponds with ratio > in Packomania's table. ------------------------------------ N = 27 > s = 15.088936116955... The best packing previously known has s = 15.088941... ------------------------------------ N = 30 s = 15.857406899747... symmetry group D_1 This is the first symmetric packing mentioned in this thread. The best packing previously known has s = 15.85759... ------------------------------------ N = 38 > s = 17.691412365977... The best packing previously known has s = 17.691412377... ------------------------------------ N = 50 > s = 20.087223055186... The best packing previously known has s = 20.08722321... ------------------------------------ N = 58 s = 21.541934648043... The best packing previously known has s = 21.541955... ------------------------------------ N = 70 > s = 23.537752475834... The best packing previously known has s = 23.5377524760... ------------------------------------ David W. Cantrell === Subject: Re: On the Origin of Religious Belief posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) God is doing gravity in the universe everywhere. Mitch Raemsch === Subject: Re: The ravages of the New Math [...] It is especially difficult for the integers; to paraphrase > Dirichlet in his famous paper, What are and what should > be the `numbers', the essential conclusion is that if it > behaves like the numbers, it is a version of them. There > are two totally different basic concepts, and then other > concepts derived from extensions. > Said famous paper Was sind und was sollen die Zahlen? > is by Dedekind, not Dirichlet. One does not get a good understanding of a concept from generalization > I strongly disagree. One often gains great insight via generalizations. > Indeed, much of abstract algebra evolved from the interplay between > concrete and general manifestations of the intuitive concept of number. I interpreted Rubin as saying that utility is not equivalent > to understanding. > My reply concerns only his above quoted remark on generalization. Right. That one finds a generalization useful does not imply > that one understands its root. Again, I see no relation to anything I said above. I said nothing about finding generalizations useful. === Subject: Re: The ravages of the New Math [...] It is especially difficult for the > integers; to paraphrase > Dirichlet in his famous paper, What are and > what should > be the `numbers', the essential conclusion is > that if it > behaves like the numbers, it is a version of > them. There > are two totally different basic concepts, and > then other > concepts derived from extensions. > Said famous paper Was sind und was sollen die > Zahlen? > is by Dedekind, not Dirichlet. One does not get a good understanding of a > concept from generalization > I strongly disagree. One often gains great > insight via generalizations. > Indeed, much of abstract algebra evolved from > the interplay between > concrete and general manifestations of the > intuitive concept of number. I interpreted Rubin as saying that utility is not > equivalent > to understanding. > My reply concerns only his above quoted remark on > generalization. Right. That one finds a generalization useful does > not imply > that one understands its root. Again, I see no relation to anything I said above. > I said nothing about finding generalizations > useful. > Then what did you mean? An example would be helpful. Tom === Subject: Re: A integral inequality for help. posting-account=UBXP6QoAAAAt4uibkeBkc4NwinZKwVk1 5.0),gzip(gfe),gzip(gfe) Problem (in ASCII) Suppose that p(t) is a C^2 function with period 2pi and it satisfies p(t) > 0, p(t) + p''(t) > 0. Prove the following inequality: int_0^2pi p(t)[p(t) + p''(t)] dt * int_0^2pi (1/(p(t) + p''(t))) dt >= 2pi int_0^2pi p(t) dt === Subject: Re: A integral inequality for help. posting-account=UBXP6QoAAAAt4uibkeBkc4NwinZKwVk1 5.0),gzip(gfe),gzip(gfe) > I don't know how to descript it in ASCII. This is a not easy . > I am sorry. Something like this: Suppose that p(t) is a C^2 function with period 2pi and it satisfies > p(t) > 0, p(t) + p''(t) > 0. Prove the followinginequality: int 0^2pi p(t)[p(t) + p''(t)] dt * int 0^2pi (1/(p(t) + p''(t))) dt = 2pi int 0^2pi p(t) dt Also prove that equality holds iff there are real constants a,b,c with > c > 0 that satisfy p(t) = a cos(t) + b sin(t) + c. That is the form of your question, unless I made some mistake. I am > not able to help with the mathematics. Somebody else will be. Note that the newsgroup convention for sub- and superscripts matches > TeX except that we may omit the braces. The letter t works better hear > than theta, so I simply used it instead. The form of int 0^2pi varies somewhat. Some might even use I 0^2pi, or > you might even be able to omit the limits and state in words that the > integrals are from 0 to 2pi. Use parentheses when putting fractions of sums on one line, like I did > above. Greater than or equal to is best written >=. The single character for > it is not in ASCII. Multiplication can be * or just put the factors next to each other, as > usual. The multiplication X or the centered dot are not in ASCII and > may or may not work depending on how people view the newsgroup and how > correctly you have identified your character code. Try to be clear of what you mean when you write and charitable when > you read the attempts by others. I will do it . === Subject: Re: Is an arbitrary multivariate polynomial equation over GF[2] ?NP-complete? >Since 1979 it is reported in the literature the NP-complete character >of the title problem. Yes, the reduction from 3SAT is an easy undergraduate exercise. It's telling > that not only are you unable to see the error in your own arguments even when > they are pointed out to you, but you can't even do this easy exercise. Hmm, it would be good to state exactly the problem. I agree that showing NP-completness of solvability of in (GF[2])^n of systems of sparse n-variate polynomials is an easy exercise. Similarely for solvability in (GF[2])^n of a single n-variate polynomial given as stright-line program. However, if one looks at single sparse polynomial situation may to be different -- I do not see how to prove that solving such equation in (GF[2])^n is NP-complete. At first glance what Valls describe may work for single equation. -- Waldek Hebisch hebisch@math.uni.wroc.pl === Subject: Showing two definite integrals are equal posting-account=tXYyDgoAAAClsCVRo58cVx83gNKWzoan AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 Safari/525.19,gzip(gfe),gzip(gfe) I'm showing that the following two definite integrals are equals: int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) I'm using substitution u = pi - x u = pi - x and x = pi - u also du = -dx -du = dx and the new limits of integration, expressed in terms of u u(0) = pi u(pi) = 0 Therefore, int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) du, pi to 0) = int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, and my book does it as follows: int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) du, pi to 0) = int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying u for the argument to sin? === Subject: Re: Showing two definite integrals are equal I'm showing that the following two definite integrals are equals: >int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) These are _not_ equal. Maybe you didn't write what > you meant? I find them equal. >I'm using substitution u = pi - x >u = pi - x and x = pi - u also >du = -dx >-du = dx and the new limits of integration, expressed in terms of u >u(0) = pi >u(pi) = 0 Therefore, >int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, >and my book does it as follows: >int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of >f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying >u for the argument to sin? David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) === Subject: Re: Showing two definite integrals are equal <2vgd05llonaet29j4r5frpt6v456pf7tfs@4ax.com> posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) >I'm showing that the following two definite integrals are equals: >int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) These are not equal. Maybe you didn't write what > you meant? I find them equal. Have you tried the function f(y) = (arcsin(y))^n for large n? R.G. Vickson I'm using substitution u = pi - x >u = pi - x and x = pi - u also >du = -dx >-du = dx and the new limits of integration, expressed in terms of u >u(0) = pi >u(pi) = 0 Therefore, >int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, >and my book does it as follows: >int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of >f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying >u for the argument to sin? David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) === Subject: Re: Showing two definite integrals are equal > I'm showing that the following two definite integrals are equals: > int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) > These are _not_ equal. Maybe you didn't write what > you meant? > I find them equal. Have you tried the function f(y) = (arcsin(y))^n for large n? I was fiddling with Maple whether it can do it. However it does not use linearity for integration, but here it is (for me it was a mess to find out the needed commands). Note the periodic is silently used by Maple via changing variables: undefine(INT);define( INT,'linear'); # linearity `expandInt`:=proc(expr) # to use linearity subs(Int=INT, expr); expand(%); subs(INT=Int,%); end proc; Int(x*f(sin(x)) , x= 0 .. Pi): %=Change(%, x = Pi-u, u): subs(u=x,%): # change variables expand(%); # expand integrand map(expandInt, %); # expand integral isolate(%, Int(f(sin(x)),x = 0 .. Pi)); # show desired Pi Pi / / | 2 | | f(sin(x)) dx = ---- | x f(sin(x)) dx | Pi | / / 0 0 === Subject: Re: Showing two definite integrals are equal posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; GTB6; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I'm showing that the following two definite integrals are equals: > int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) I'm using substitution u = pi - x > u = pi - x and x = pi - u also > du = -dx > -du = dx and the new limits of integration, expressed in terms of u > u(0) = pi > u(pi) = 0 Therefore, > int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) > du, pi to 0) > = int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, > and my book does it as follows: > int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) > du, pi to 0) > = int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of > f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying > u for the argument to sin? Use the formula for sin(a - b). Dave === Subject: Re: Showing two definite integrals are equal > I'm showing that the following two definite integrals are equals: > int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) I'm using substitution u = pi - x > u = pi - x and x = pi - u also > du = -dx > -du = dx and the new limits of integration, expressed in terms of u > u(0) = pi > u(pi) = 0 Therefore, > int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) > du, pi to 0) > = int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, > and my book does it as follows: > int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) > du, pi to 0) > = int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of > f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying > u for the argument to sin? Use the formula for sin(a - b). I find it simpler to just visualize sin(pi - u) = sin(u). > Dave === Subject: Re: Showing two definite integrals are equal >I'm showing that the following two definite integrals are equals: >int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) I'm using substitution u = pi - x >u = pi - x and x = pi - u also >du = -dx >-du = dx and the new limits of integration, expressed in terms of u >u(0) = pi >u(pi) = 0 Therefore, >int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, >and my book does it as follows: >int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of >f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying >u for the argument to sin? Is there a trig identity relating sin(pi - t) to sin(t) ? === Subject: Re: Showing two definite integrals are equal posting-account=tXYyDgoAAAClsCVRo58cVx83gNKWzoan AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.59 Safari/525.19,gzip(gfe),gzip(gfe) >I'm showing that the following two definite integrals are equals: >int(x*f(sin(x)) dx, 0 to pi) = (pi/2) * int(f(sin(x)) dx, 0 to pi) I'm using substitution u = pi - x >u = pi - x and x = pi - u also >du = -dx >-du = dx and the new limits of integration, expressed in terms of u >u(0) = pi >u(pi) = 0 Therefore, >int( x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(pi - u) ) du, 0 to pi) At this point, I checked my book, because I was stuck, >and my book does it as follows: >int(x * f( sin(x) ) dx, 0 to pi) = -int( (pi - u) * f( sin(pi - u) ) >du, pi to 0) >= int( (pi - u) * f( sin(u) ) du, 0 to pi) The last definite integral above has f( sin(u) ) instead of >f( sin(pi - u) ) How can we go from saying pi - u (because x = pi - u) to saying >u for the argument to sin? Is there a trig identity relating sin(pi - t) to sin(t) ? Yeah, I can't believe I overlooked that. Two things puzzle me now. 1) Others are claiming they are not equal. (This is from my book. Thus, is my book mistaken here?) 2) The next step my book shows, in showing that the above are equal: -int( (pi - u) * f( sin(pi-u) ) du, pi to 0) = int( (pi - u) * f( sin(u) ) du, 0 to pi) = pi*int( f(sin(u)) du, 0 to pi) - int( u * f(sin(u)) du, 0 to pi) = pi*int( f(sin(x)) dx, 0 to pi) - int( x * f(sin(x)) dx, 0 to pi) and that this somehow implies the following: 2*int(x * f(sin(x)) dx, 0 to pi) = pi*int( f(sin(x) dx, 0 to pi) It's as though they are applying a symmetric property to int( x * f(sin(x)) dx, 0 to pi) but I don't see how it is justified. I think I would understand if the limits of integration were -pi to pi instead of 0 to pi. Any clarification welcomed. === Subject: Re: A differential functional equation > f(x,y) is a real function R^2->R ,y in R - {0} , x in R And we' ve got f(x +1,y) = d/dy f(x,y) - 2*f(x,y)/y How can we manage such a thing? Any idea is welcome, > Alain > Here's a fairly general solution: f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! where g(x) is any function of your choice. Bob === Subject: Re: A differential functional equation f(x,y) is a real function R^2->R ,y in R - {0} , x in R And we' ve got f(x +1,y) = d/dy f(x,y) - 2*f(x,y)/y How can we manage such a thing? Any idea is welcome, > Alain > Here's a fairly general solution: f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! where g(x) is any function of your choice. Bob I should have said: where g(x) is any function of your choice for which the infinite series converges absolutely and uniformly. Bob === Subject: Re: A differential functional equation <090520092156548851%delaneyrm@earthlink.net> <090520092250317725%delaneyrm@earthlink.net> posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) > f(x,y) is a real function R^2->R ,y in R - {0} , x in R And we' ve got f(x +1,y) = d/dy f(x,y) - 2*f(x,y)/y How can we manage such a thing? Any idea is welcome, > Alain Here's a fairly general solution: f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! where g(x) is any function of your choice. Bob I should have said: where g(x) is any function of your choice for which the infinite series > converges absolutely and uniformly. Bob- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonjour Bob, Do you mind explaining how you did arrive at this fairly general solution, I will give you my building Alain === Subject: Re: A differential functional equation > f(x,y) is a real function R^2->R ,y in R - {0} , x in R And we' ve got f(x +1,y) = d/dy f(x,y) - 2*f(x,y)/y How can we manage such a thing? Any idea is welcome, > Alain Here's a fairly general solution: f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! where g(x) is any function of your choice. Bob I should have said: where g(x) is any function of your choice for which the infinite series > converges absolutely and uniformly. Bob- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonjour Bob, Do you mind explaining how you did arrive at this > fairly general solution, I will give you my building Alain Alain, Assume: f(x, y) = Sum(n=0 to inf) a_n(x) y^n {1} Putting this into your equation gives: Sum(n=0 to inf) a_n(x+1) y^n = Sum(n=0 to inf) (n-2) a_n(x) y^(n-1) (2) so Sum(n=0 to inf) a_n(x+1) y^n = -2 a_0(x) y^(-1) - a_1(x) + Sum(n=3 to inf) (n-2) a_n(x) y^(n-1) (3) Since there is no y^(-1) term on the left a_0(x) = 0 (all x) (4) So Sum(n=1 to inf) a_n(x+1) y^n = - a_1(x) + Sum(n=3 to inf) (n-2) a_n(x) y^(n-1) (5) But now there is no y^0 = 1 term on the left, so a_1(x) = 0 (all x) (6) So: Sum(n=2 to inf) a_n(x+1) y^n = Sum(n=3 to inf) (n-2) a_n(x) y^(n-1) (7) On the right let n -> n+1 Sum(n=2 to inf) a_n(x+1) y^n = Sum(n=2 to inf) (n-1) a_(n+1)(x) y^n (8) a_n(x+1) = (n-1) a_(n+1)(x) n = 2, 3, ... (9) Rewrite this as: a_(n+1)(x) = a_n(x+1) / (n-1) n = 2, 3, ... (10) n = 2 a_3(x) = a_2(x+1) = g(x+1) (so a_2(x) = g(x) ) n = 3 a_4(x) = a_3(x+1) / 2 = g(x+2) / 2 n = 4 a_5(x) = a_4(x+1) / 3 = g(x+3) / 3! . . . so we see a_n(x) = g(x+n-2) / (n-2)! n = 2, 3, 4, ... and a_0(x) = a_1(x) = 0 Put this back into (1): f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! (11) and there's my fairly general solution. Bob === Subject: Re: A differential functional equation <090520092156548851%delaneyrm@earthlink.net> <090520092250317725%delaneyrm@earthlink.net> <100520090640382593%delaneyrm@earthlink.net> posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) f(x,y) is a real function R^2->R ,y in R - {0} , x in R And we' ve got f(x +1,y) = d/dy f(x,y) - 2*f(x,y)/y How can we manage such a thing? Any idea is welcome, > Alain Here's a fairly general solution: f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! where g(x) is any function of your choice. Bob I should have said: where g(x) is any function of your choice for which the infinite series > converges absolutely and uniformly. Bob- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonjour Bob, Do you mind explaining how you did arrive at this > fairly general solution, I will give you my building Alain Alain, Assume: f(x, y) = Sum(n=0 to inf) a n(x) y^n {1} Putting this into your equation gives: Sum(n=0 to inf) a n(x+1) y^n = Sum(n=0 to inf) (n-2) a n(x) y^(n-1) (2) so Sum(n=0 to inf) a n(x+1) y^n = -2 a 0(x) y^(-1) - a 1(x) + Sum(n=3 to > inf) (n-2) a n(x) y^(n-1) (3) Since there is no y^(-1) term on the left a 0(x) = 0 (all x) (4) So Sum(n=1 to inf) a n(x+1) y^n = - a 1(x) + Sum(n=3 to inf) (n-2) a n(x) > y^(n-1) (5) But now there is no y^0 = 1 term on the left, so a 1(x) = 0 (all x) (6) So: Sum(n=2 to inf) a n(x+1) y^n = Sum(n=3 to inf) (n-2) a n(x) y^(n-1) (7) On the right let n -> n+1 Sum(n=2 to inf) a n(x+1) y^n = Sum(n=2 to inf) (n-1) a (n+1)(x) y^n > (8) > a n(x+1) = (n-1) a (n+1)(x) n = 2, 3, ... (9) Rewrite this as: a (n+1)(x) = a n(x+1) / (n-1) n = 2, 3, ... (10) n = 2 > a 3(x) = a 2(x+1) = g(x+1) (so a 2(x) = g(x) ) n = 3 > a 4(x) = a 3(x+1) / 2 = g(x+2) / 2 n = 4 > a 5(x) = a 4(x+1) / 3 = g(x+3) / 3! . > . > . > so we see a n(x) = g(x+n-2) / (n-2)! n = 2, 3, 4, ... and a 0(x) = a 1(x) = 0 Put this back into (1): f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! (11) and there's my fairly general solution. Bob- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonsoir Bob, I will propose you three different homemade solutions: f1(x,y) = k*y^2*a^x*exp(a*y) , f3(x,y) = k*y^2*sin(y+Pi*x/2) All built from a formal form using partial derivation :f(x,y) = k*y^2*(d/dy)^(x) o g(y) k a constant , Alain === Subject: Re: A differential functional equation f(x,y) is a real function R^2->R ,y in R - {0} , x in R And we' ve got f(x +1,y) = d/dy f(x,y) - 2*f(x,y)/y How can we manage such a thing? Any idea is welcome, > Alain Here's a fairly general solution: f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! where g(x) is any function of your choice. Bob I should have said: where g(x) is any function of your choice for which the infinite series > converges absolutely and uniformly. Bob- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonjour Bob, Do you mind explaining how you did arrive at this > fairly general solution, I will give you my building Alain Alain, Assume: f(x, y) = Sum(n=0 to inf) a_n(x) y^n {1} Putting this into your equation gives: Sum(n=0 to inf) a_n(x+1) y^n = Sum(n=0 to inf) (n-2) a_n(x) y^(n-1) (2) so Sum(n=0 to inf) a_n(x+1) y^n = -2 a_0(x) y^(-1) - a_1(x) + Sum(n=3 to > inf) (n-2) a_n(x) y^(n-1) (3) Since there is no y^(-1) term on the left a_0(x) = 0 (all x) (4) So Sum(n=1 to inf) a_n(x+1) y^n = - a_1(x) + Sum(n=3 to inf) (n-2) a_n(x) > y^(n-1) (5) But now there is no y^0 = 1 term on the left, so a_1(x) = 0 (all x) (6) So: Sum(n=2 to inf) a_n(x+1) y^n = Sum(n=3 to inf) (n-2) a_n(x) y^(n-1) (7) On the right let n -> n+1 Sum(n=2 to inf) a_n(x+1) y^n = Sum(n=2 to inf) (n-1) a_(n+1)(x) y^n > (8) > a_n(x+1) = (n-1) a_(n+1)(x) n = 2, 3, ... (9) Rewrite this as: a_(n+1)(x) = a_n(x+1) / (n-1) n = 2, 3, ... (10) n = 2 > a_3(x) = a_2(x+1) = g(x+1) (so a_2(x) = g(x) ) n = 3 > a_4(x) = a_3(x+1) / 2 = g(x+2) / 2 n = 4 > a_5(x) = a_4(x+1) / 3 = g(x+3) / 3! . > . > . > so we see a_n(x) = g(x+n-2) / (n-2)! n = 2, 3, 4, ... and a_0(x) = a_1(x) = 0 Put this back into (1): f(x, y) = Sum(n=2 to inf) g(x+n-2) y^n / (n-2)! (11) and there's my fairly general solution. Bob- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonsoir Bob, I will propose you three different homemade solutions: > f1(x,y) = k*y^2*a^x*exp(a*y) , > f3(x,y) = k*y^2*sin(y+Pi*x/2) All built from a formal form using partial > derivation :f(x,y) = k*y^2*(d/dy)^(x) o g(y) k a constant , Alain Alain, In my solution, factor out y^2 and let n -> n+2: f(x, y) = y^2 Sum(n=0 to inf) g(x+n) y^n / n! (1) Take g(x) = k a^x Then f(x, y) = k y^2 Sum(n=0 to inf) a^(x+n) y^n / n! f(x, y) = k y^2 a^x Sum(n=0 to inf) (a*y)^n / n! f(x, y) = k y^2 a^x exp(a*y) (2) which is your f1(x, y). Next take: g(x) = k exp(i Pi*x/2) (3) This leads to: f(x, y) = k y^2 exp(i Pi*x/2) Sum(n=0 to inf) (y*exp(i Pi/2)^n / n! But exp(i Pi/2) = i , so f(x, y) = k y^2 exp(i Pi*x/2) Sum(n=0 to inf) (i*y)^n / n! f(x, y) = k y^2 exp(i Pi*x/2) exp(i*y) f(x, y) = k y^2 exp[i*(y + Pi*x/2)] f(x, y) = k y^2 cos(y + Pi*x/2) + i k y^2 sin(y + Pi*x/2) which gives two real solutions, your f3(x, y) and f4(x, y) = k y^2 cos(y + Pi*x/2) I don't immediately see what g(x) gives your f2(x, y). Bob === Subject: Re: Point charges inside a sphere I find the results truly beautiful. The fact that even though the charge > density on the sphere (or circle) continues to climb as new charges are > added - there is never a time when it's better to place one of the > charges internally is very nice. But, as I noted earlier in the thread, that's _not_ true if we're dealing with a circular disk. To clarify: I'm not a physicist; I assume that the corresponding mathematical problem is minimization of the sum of reciprocals of distances between pairs of points. Given 12 or more points on a circular disk, minimizing that sum requires that some of the points lie _in the interior_ of the disk. David W. Cantrell > I was hoping to get some hint as to the field of mathematics involved in > deriving which configurations are optimal - in practice numerical > optimization will give the results & a bit of work will show that they > are locally stable. Is there a neater way? A question I need some guidance in answering (relevant math skills in >need of a dust off). n like charges are confined to the inside of a sphere. My intuition > says that the relevant electric potential is minimised by the following > charge configurations: n=2 two charges diametrically opposit (though the diameter might > obviously be moving) > n=3 tree charges coplanar and at the vertices of an equilateral > triangle (again possibly in motion) > n=4 four charges at the verices of a tetrahedron (also possibly in > motion) n=6 six charges at the vertices of an octohedron (ditto) > n=8 eight charges at the verices of a cube (ditto). 1) How to prove this short of brute force algebra? > 2) What are the configurations that minimise the electric potential > when n = 5, or 7 (or 9, 10,11, ...)? > === Subject: Re: Point charges inside a sphere > I find the results truly beautiful. The fact that even though the charge > density on the sphere (or circle) continues to climb as new charges are > added - there is never a time when it's better to place one of the > charges internally is very nice. But, as I noted earlier in the thread, that's _not_ true if we're dealing > with a circular disk. To clarify: > I'm not a physicist; I assume that the corresponding mathematical problem > is minimization of the sum of reciprocals of distances between pairs of > points. Given 12 or more points on a circular disk, minimizing that sum > requires that some of the points lie _in the interior_ of the disk. David W. Cantrell I've been trying to understand things in terms of potential theory and harmonic functions. In two dimensions, I think U(x, y) = log( sqrt(x^2 + y^2) ) satisfies Laplace's equation ( del^2 /del x^2 + del^2 /del y^2 ) U == 0 , except at (0, 0). So for example with 12 point-charges in the unit disk, D = {(x,y): x^2+y^2 <= 1}, with position vectors u_1, u_2, ... u_12, one asks to maximize sum_{1<=i < j <=12} ( log ( || u_i - u_j ||_2 ) ), (***) so ||.|| is the Euclidean norm. Then I'm wondering if all 12-point configurations that maximize the function (***) will have u_1, u_2, ... on the unit circle, or if some can be in the interior of D, D being a closed set for R^2 in the usual sense. Cf. Maximum Principle, http://en.wikipedia.org/wiki/Harmonic_function David > I was hoping to get some hint as to the field of mathematics involved in > deriving which configurations are optimal - in practice numerical > optimization will give the results & a bit of work will show that they > are locally stable. Is there a neater way? > A question I need some guidance in answering (relevant math skills in > need of a dust off). n like charges are confined to the inside of a sphere. My intuition > says that the relevant electric potential is minimised by the following > charge configurations: n=2 two charges diametrically opposit (though the diameter might > obviously be moving) > n=3 tree charges coplanar and at the vertices of an equilateral > triangle (again possibly in motion) > n=4 four charges at the verices of a tetrahedron (also possibly in > motion) n=6 six charges at the vertices of an octohedron (ditto) > n=8 eight charges at the verices of a cube (ditto). 1) How to prove this short of brute force algebra? > 2) What are the configurations that minimise the electric potential > when n = 5, or 7 (or 9, 10,11, ...)? > === Subject: Re: combinations and cutting stock problem posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > My question is basically, is there standard code routines to assemble > all combinations of a list of unique numbers where the list of numbers > have different quantities. This would be a flat list similar to: 1 1 1 2 > 2 4 4 4 8 8 8 8 8 9 14 15 15 etc. I am doing a 'cutting stock problem' scenerio. The combination code for > I arrived at seemed a little linear and since it's rather new to me > maybe there's better solutions. There is a huge literature on the cutting-stock problem, including linear programming formulations, dynamic programming methods, etc. You seem to be trying to re-invent the wheel, and maybe not in the best way. Look at http://en.wikipedia.org/wiki/Cutting stock problem . In many problems you don't need to generate all the patterns; the seminal work of Gilmore and Gomory shows how to use a knapsack problem to generate patterns only as needed (in a somewhat limited version of the problem, admittedly). The paper in http://or.journal.informs.org/cgi/content/abstract/13/1/94 deals with a two-dimensional version; you can see the abstract for free, and below that see a list of other papers that cite this one. Many of these newer works deal with quite general versions; in particular, look at the Chu and Antonio paper (last in the citation list). This works nice but doesn't scale too well in my opinion. It eventually > will go into a database and I'd like to use database scalability. with an array or list of 'finish' lengths in ascending order. > add to the first finish, check total length and if less than 'stock' > length record the qnt of finish lengths needed for each iteration > when it exceeds the stock length return to 0 qnt and do a carry carry is function that: > advances to next finish length and increments it. If no more finish > lengths signal done. > check total length and if less than stock do like above > if over then mark as zero qnt and recurse into another carry. I'm not really sure exactly what your algorithm is attempting to do and what you are trying to achieve: cost minimization? minimum wastage? reduced inventory? Most real problems of this type do not do very well in the type of list-processing procedure that you seem to be using. Optimization techniques often yield *much* better solutions. Some very effective heuristics are available in cases that are too large to be solved to optimality. These are actually used in real industrial situations such as paper cutting, glass cutting, etc. Variants are even used in the garment industry; see the famous paper Blue Bell Trims its Inventory, by Edwards, Wagner and Wood, Interfaces, Vol. 15 (1985), pp. 34-52. There is a lot out there; you would be wise to look into it. R.G. Vickson check total is a routine that: > loops through all the finish qnts to calculate the total being used. -- > Phil === Subject: Re: combinations and cutting stock problem There is a lot out there; you would be wise to look into it. R.G. Vickson > check total is a routine that: > loops through all the finish qnts to calculate the total being used. -- > Phil === Subject: Re: EMIS has my old paper back up? > Looks like EMIS has my paper back: So now you cannot state that sci.math'rs blocked your paper., Now, You cannot state that Mathematicians blocked your paper However, You can clearly state that your paper is self-blocking. JSH submitting his paper; http://cache.gizmodo.com/assets/images/gizmodo/2008/09/DogPoop.jpg James Harris === Subject: Re: EMIS has my old paper back up? > Looks like EMIS has my paper back: > We'll make sure it's removed as soon as possible, you blithering fountain of non-stop idiocy. We've already been in contact with the webmaster and the local law enforcement departments. === Subject: Re: JSH: EMIS has my old paper back up? posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) > Looks like EMIS has my paper back: Here I'm curious as to whether or not anyone knows why it'd be back up > now. > It was incorrect and therefore an inconsequential paper, so why would anyone waste any more time caring about this paper or giving it any further thought? Oh yeah, those wondering how crappy this paper really is given the > drama around it can now see it for themselves, if that link works. > (It worked just now when I noticed it.) > What is so funny (well, really it's more pathetic, I suppose) is about how you taut the paper's quality, not having one clue as to how absolutely terrible it is. Your submission is so poor, it wouldn't even get a passing grade as paper submitted for an undergraduate project. People have made LISTS of what is wrong with this piece of crap paper, and you're so dumb, you are *still* clueless. As proof, let's just see if there is ONE person who will be able to objectively claim it isn't crappy. Any takers?? M === Subject: Re: JSH: EMIS has my old paper back up? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Here I'm curious as to whether or not anyone knows why it'd be back up > now. It was incorrect and therefore an inconsequential paper, so why would > anyone waste any more time caring about this paper or giving it any > further thought? I had never seen the paper, but my curiosity on JSH's production has never been great so I had no motivation to hunt for it. Now that he's offered a link, well, I did look... It is quite amazing that anyone thought that text was publishable, even without taking into account its actual mathematical content---which is null. I was amused to find even an inverted question mark on page 8, which in all likelyhood comes from the fact that the text was emailed and that the corresponding line in the .tex file, which started with to prevent it from being misinterpreted by email/usenet software, and that >, in turn, got interpreted by TeX as an inverted question mark (as per the default character encoding used by modern TeX) Such attention to detail surely goes all the way from the care on the text to the mathematical reasoning! -- m === Subject: Re: JSH: EMIS has my old paper back up? sha1:XgPlTbDH1+eWnH0QqunDJz0S8MI= > It is interesting that you think so though, but readers considering > this issue now years later know that extraordinary things happened > after that publication: sci.math'ers mounted an email assault > against it, the editors caved and yanked the paper after > publication[...] This email assault... how many emails do you think were sent? I recall one publicly mentioned here on sci.math for certain, and I think that there was a second one, but my memory is faulty. Do you think that there were more than two? Dozens? Hundreds? You sure make it sound like a large and organized campaign. I just wonder how big you think it is. -- Jesse F. Hughes Baba: Spell checkers are bad. Quincy (age 7): C-H-E-K-E-R-S A-R-E B-A-D. === Subject: Re: JSH: EMIS has my old paper back up? On May 9, 5:10 pm, Mariano Su.87rez-Alvarez paper back: > Here I'm curious as to whether or not anyone knows why it'd be back up > now. It was incorrect and therefore an inconsequential paper, so why would > anyone waste any more time caring about this paper or giving it any > further thought? I had never seen the paper, but my curiosity on > JSH's production has never been great so I had > no motivation to hunt for it. Now that he's > offered a link, well, I did look... It is quite > amazing that anyone thought that text was publishable, ** it really is an incomplete and immature mess, like a first grader in highschool. Not really. What I did was find a novel way to prove that some foundational views in number theory are wrong. Someone believing that true might treat the paper, um, rather like a historical artifact. ** Sorry bub, it is worthless garbage, and usless. > even without taking into account its actual mathematical > content---which is null. I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! That's a non sequitur. Minor typographical errors do not prove a mathematical line of reasoning to be flawed. ** the paper is nonsence, troll. It is interesting that you think so though, but readers considering this issue now years later know that extraordinary things happened after that publication: sci.math'ers mounted an email assault against it, the editors caved and yanked the paper after publication, they managed one more edition of the journal and then quietly shut down, but even weirder, its hosting university, Cameron University then scrubbed ALL MENTION of the journal from its websites!!! **as they should. They trashed a decades worth of papers, which should be disquieting to people who publish in electronic only journals. EMIS saved its archives though, and now it seems saw fit to save my paper as well. Discounting all of that over typos indicates you are very much, um, not rational. That paper historically may be considered one of the biggest in mathematical history. ** lying troll. Deference to it by the editors will not seem strange to historians. Leaving in minor errors might have seemed like the best thing to do to the editors, kind of like, how dare you correct something that huge? But then they went into shock at the reaction of their community, and fell apart. **they did not read it, it is crap, meaningless drival from an idiot troll on the internet. Your mathematical community betrayed their trust, and destroyed a journal in the process. You broke your own rules. James Harris Pix of JSH at home working; http://i15.photobucket.com/albums/a386/Smashingions/Kim_Jong_Ill.jpg === Subject: Re: JSH: EMIS has my old paper back up? posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > On May 9, 5:10pm, Mariano Su.87rez-Alvarez > Here I'm curious as to whether or not anyone knows why it'd be back up > now. It was incorrect and therefore an inconsequential paper, so why would > anyone waste any more time caring about this paper or giving it any > further thought? I had never seen the paper, but my curiosity on > JSH's production has never been great so I had > no motivation to hunt for it. Now that he's > offered a link, well, I did look... It is quite > amazing that anyone thought that text was publishable, Not really. What I did was find a novel way to prove that some > foundational views in number theory are wrong. Someone believing that true might treat the paper, um, rather like a > historical artifact. even without taking into account its actual mathematical > content---which is null. I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! That's a non sequitur. Minor typographical errors do not prove a > mathematical line of reasoning to be flawed. It is interesting that you think so though, but readers considering > this issue now years later know that extraordinary things happened > after that publication: sci.math'ers mounted an email assault against > it, the editors caved and yanked the paper after publication, they > managed one more edition of the journal and then quietly shut down, > but even weirder, its hosting university, Cameron University then > scrubbed ALL MENTION of the journal from its websites!!! They trashed a decades worth of papers, which should be disquieting to > people who publish in electronic only journals. EMIS saved its archives though, and now it seems saw fit to save my > paper as well. Discounting all of that over typos indicates you are very much, um, > not rational. That paper historically may be considered one of the biggest in > mathematical history. Deference to it by the editors will not seem strange to historians. Leaving in minor errors might have seemed like the best thing to do to > the editors, kind of like, how dare you correct something that huge? > But then they went into shock at the reaction of their community, and > fell apart. Your mathematical community betrayed their trust, and destroyed a > journal in the process. You broke your own rules. James Harris- Hide quoted text - - Show quoted text - Submit your paper to a print journal under a pseudonym. Leave out explicit statements that it proves there are errors in the foundations of number theory. Wait until your paper is published and irretrievably distributed in printed copies of the journal. Write another paper under your real name, citing your earlier paper, showing that there are errors in the foundations of number theory. The evil, lying mathematicians won't have a chance. Enrico === Subject: Re: JSH: EMIS has my old paper back up? posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On May 9, 7:10pm, Mariano Su.87rez-Alvarez > I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! Actually, the most common source of that particular problem occurs when, while typing the *.tex source, one inadvertedly types > instead of ., usually because the immediate prior character requires the shift key. It happens to me a lot when a period follows an in- line formula (which ends in $). It's appearance does indicate a very lacking process of proof-reading, however. -- Arturo Magidin === Subject: Re: JSH: EMIS has my old paper back up? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > On May 9, 7:10pm, Mariano Su.87rez-Alvarez I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! Actually, the most common source of that particular problem occurs > when, while typing the *.tex source, one inadvertedly types instead of ., usually because the immediate prior character requires > the shift key. It happens to me a lot when a period follows an in- > line formula (which ends in $). Hmm. That may be the case in an USian keyboard layout, I guess. starts a paragraph)... I wonder what Holmes did when after removing the impossible *two* options remained! ;-) > It's appearance does indicate a very lacking process of proof-reading, > however. Indeed. -- m === Subject: Re: JSH: EMIS has my old paper back up? posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On May 9, 10:48pm, Mariano Su.87rez-Alvarez Actually, the most common source of that particular problem occurs > when, while typing the *.tex source, one inadvertedly types instead of ., usually because the immediate prior character requires > the shift key. It happens to me a lot when a period follows an in- > line formula (which ends in $). Hmm. That may be the case in an USian keyboard layout, I guess. The usual keyboard (US) does not have an opening question mark. Regular TeX typesets < outside of math mode as the opening question mark (I was wrong above; it's not >, and it usually shows up, for me, when trying to write a comma right after a dollar sign). > starts a paragraph)... I wonder what Holmes did when after > removing the impossible *two* options remained! ;-) I'm pretty sure it is the result of an errant > in the source file. why it was there, well, there are so many things to wonder about that particular TeX file... -- Arturo Magidin === Subject: Re: JSH: EMIS has my old paper back up? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > On May 9, 10:48pm, Mariano Su.87rez-Alvarez > Actually, the most common source of that particular problem occurs > when, while typing the *.tex source, one inadvertedly types instead of ., usually because the immediate prior character requires > the shift key. It happens to me a lot when a period follows an in- > line formula (which ends in $). Hmm. That may be the case in an USian keyboard layout, I guess. The usual keyboard (US) does not have an opening question mark. > Regular TeX typesets < outside of math mode as the opening question > mark (I was wrong above; it's not >, and it usually shows up, for > me, when trying to write a comma right after a dollar sign). Run tex on the file %%% cut here >< bye %%% cut here -- m === Subject: Re: JSH: EMIS has my old paper back up? posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On May 9, 11:09pm, Mariano Su.87rez-Alvarez On May 9, 10:48pm, Mariano Su.87rez-Alvarez > Actually, the most common source of that particular problem occurs > when, while typing the *.tex source, one inadvertedly types instead of ., usually because the immediate prior character requires > the shift key. It happens to me a lot when a period follows an in- > line formula (which ends in $). Hmm. That may be the case in an USian keyboard layout, I guess. The usual keyboard (US) does not have an opening question mark. > Regular TeX typesets < outside of math mode as the opening question > mark (I was wrong above; it's not >, and it usually shows up, for > me, when trying to write a comma right after a dollar sign). Run tex on the file %%% cut here>< bye > %%% cut here LaTeX on a file whose document body contains a line with nothing but >< followed by a line with nothing but <> produces a line with Ë' and then a line with 'Ë. So, yes, it's > that produces the opening question mark, and < that produces the opening exclamation mark, when typeset outside of math mode. -- Arturo Magidin === Subject: Re: JSH: EMIS has my old paper back up? posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On May 9, 6:10pm, Mariano Su.87rez-Alvarez Here I'm curious as to whether or not anyone knows why it'd be back up > now. It was incorrect and therefore an inconsequential paper, so why would > anyone waste any more time caring about this paper or giving it any > further thought? I had never seen the paper, but my curiosity on > JSH's production has never been great so I had > no motivation to hunt for it. Now that he's > offered a link, well, I did look... It is quite > amazing that anyone thought that text was publishable, > even without taking into account its actual mathematical > content---which is null. I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! -- m I don't have PostScript - Last time I looked, it costs way too much. Is there any other way to view this file? Enrico === Subject: Re: JSH: EMIS has my old paper back up? I don't have PostScript - Last time I looked, it costs way too much. Is there any other way to view this file? > Enrico There is an online PostScript viewer at http://view.samurajdata.se/ if you don't want to install GhostScript. rossum === Subject: Re: JSH: EMIS has my old paper back up? posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) >I don't have PostScript - Last time I looked, it costs way too much. Is there any other way to view this file? Enrico There is an online PostScript viewer athttp://view.samurajdata.se/if > you don't want to install GhostScript. rossum I have stashed the information in my software folder and bookmarked the online PostScript viewer, which works fine. Unreadable PostScript files on technical sites have bugged me for years - Now, if I can just find them again ... Amazing what you can learn by reading JSH threads! Enrico === Subject: Re: JSH: EMIS has my old paper back up? > On May 9, 6:10 pm, Mariano Su.87rez-Alvarez > Here I'm curious as to whether or not anyone knows why it'd be back up > now. > It was incorrect and therefore an inconsequential paper, so why would > anyone waste any more time caring about this paper or giving it any > further thought? > I had never seen the paper, but my curiosity on > JSH's production has never been great so I had > no motivation to hunt for it. Now that he's > offered a link, well, I did look... It is quite > amazing that anyone thought that text was publishable, > even without taking into account its actual mathematical > content---which is null. I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! > -- m I don't have PostScript - Last time I looked, it costs way too much. Is there any other way to view this file? > Enrico Linux has PostScript viewers. Many Linux distributions offer Live CD versions. With a LiveCD, one has to tell the computer to boot from a CD by changing the setting in the BIOS ( the order of boot devices: 1st, 2nd, 3rd, ...). With a LiveCD, Linux goes in random access memory, and is not written to any hard drive. After using the LiveCD, the BIOS settings can be changed to what they were previously (e.g. 1st boot device = hard drive). The file to download is called an image file and its name ends with .iso. Then Nero can burn it to a CD. For example, Ubuntu has a LiveCD for version 8.04 : https://help.ubuntu.com/community/LiveCD Whether you can add the PostScript viewer depends on how much a chance you can add a PostScript viewer. David Bernier === Subject: Re: JSH: EMIS has my old paper back up? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > On May 9, 6:10pm, Mariano Su.87rez-Alvarez > Here I'm curious as to whether or not anyone knows why it'd be back up > now. It was incorrect and therefore an inconsequential paper, so why would > anyone waste any more time caring about this paper or giving it any > further thought? I had never seen the paper, but my curiosity on > JSH's production has never been great so I had > no motivation to hunt for it. Now that he's > offered a link, well, I did look... It is quite > amazing that anyone thought that text was publishable, > even without taking into account its actual mathematical > content---which is null. I was amused to find even an > inverted question mark on page 8, which in all likelyhood > comes from the fact that the text was emailed and that the > corresponding line in the .tex file, which started with > to prevent it from being misinterpreted by email/usenet > software, and that >, in turn, got interpreted by TeX > as an inverted question mark (as per the default character > encoding used by modern TeX) Such attention to detail > surely goes all the way from the care on the text to the > mathematical reasoning! -- m I don't have PostScript - Last time I looked, it costs way too much. Is there any other way to view this file? Install ghostscript. -- m === Subject: Re: A nonselfadjoint problem <9fz1SQEiE3gUSLjiV9fX8PTKDXYo@4ax.com> posting-account=Z5htrQoAAACb1B0y8lJrX3mUp3bNgmb- MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 1.1.4322; MS-RTC LM 8),gzip(gfe),gzip(gfe) >I already correctly solved the BVP, so there is no need to repeat >that. Lambdas are complex as well as eigenfunctions. One more time BVP with additional constants (since one of them is >critical) just to make sure we are on the same page: U''(x) ? ((lambda^2)/(c^2))* U(x) = 0 0< x < L U'(0) = d1*lambda*U(0)/c >U'(L) = - d2*lambda*U(L)/c d1,d2,c,L are constants. d1 is critical since if it is 1, a certain ln >[(1-d1) * ....)] term does not like it. So, for now we can assume d1 >to be nice ( 0 < d1 <1 and other constants positive). Now, the problem is to use those eigenfunctions with IC to obtain the >coefficients of the series. u(x,0) = g(x) = Re{ Sum[(C n+i*D n)*Un(x)* exp(lambda n * >t))] } >u t(x,0) = f(x) = Re { Sum[lambda n*(C n+i*D n)*Un(x)* exp(lambda n * >t))] } where Un(x) is the n-th eigenfunction, lambda n n-th characteristic >value, and C n and D n n-th constants. Normally, one would multiply equations for ICs with n-th eigenfunction >and integrate from 0 to L to obtain C n and D n, but the >eigenfunctions are not orthogonal and n-th term cannot be isolated, so >this is useless, plus for this PDE variables separate in complex >domain, so we have to work in there. Yes, that is a problem and I don't have any answer for you. Not sure I > can be of much help to you at this point. Unless I made a mistake in > my previous post, you don't have a discrete set of eigenvalues anyway. Maybe there's a PDE pro watching who can jump in. --Lynn http://math.asu.edu/~kurtz- Hide quoted text - - Show quoted text - No need for PDE pro. I solved the problem with this approach. One has to find a linear operator that includes this BVP, then finds the adjoint of that new operator which will only be formally self-adjoint, but the orthogonality will be available with expansion theorem, which then can be applied to IC to obtain the series coefficients. It is amazing how a little problem like this can span a whole range of issues and make one learn a lot of math:) === Subject: Re: a.s. question > In seems that your reasoning works even when the random sequence has > exponential distribution... or not? Laurence Not. For an exponential distribution, P{(c+epsilon) t > X > (c-epsilon) t} > P(X > (c+epsilon) t) if t is large enough. In fact, by the lack of memory property P((c+epsilon) t > X > (c-epsilon) t) > P(X > (c+epsilon) t) iff P(2 epsilon t > X) > 1/2. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Alan Schwartz Jewish science in full-bloom posting-account=LbmTuwoAAADoHbYhEeDizu-5Xkpx1kib Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) One must really consider Tom's history on Usenet. he has systematically denied any Anti-Semitism. recently in a parallell group he referred me to the following site - you can read my reply. The site implies that David Irving (amongst others is a victim of some sort of Jewish conspiracy: please read the judgement oj Justice Gray whilst bearing in mind that Irving himself brought the case. > for expressing facts about Jews visit the following web site.http://www.zundelsite.org/english/debate/victims/index.html > That is a lovely site, Tom. Read a little about one of the poor > victims! > Irving 'sang racist poem to daughter in her pram' > By Sandra Laville > IrvingDavid Irving: recorded the 'racist' poem in his diary DAVID > IRVING, the historian, was accused in the High Court yesterday of > being a perverted racist who taught his daughter a poisonous poem > diary, was labelled a racist ditty by the defence QC, who said Mr > Irving sang it to his nine-month-old daughter when half-breed > children were wheeled by in prams. > Richard Rampton, defending Deborah Lipstadt, an American academic, and > Penguin Books, produced the entry from September 1994, as he cross- > examined Mr Irving. > The verse read: I am a Baby Aryan / Not Jewish or Sectarian / I have > no plans to marry an / Ape or Rastafarian. > In an increasingly heated exchange Mr Rampton asked: Racist, Mr > Irving? Anti-Semitic, Mr Irving? > Mr Irving replied: I don't think so. > Mr Rampton: Teaching your little child this kind of poison? > Mr Irving: Do you think a nine-month-old can understand? > To laughter in the courtroom, Mr Rampton said that when he was six > months old the only kind of ditty he sang was pussy's in the apple > tree until she thinks it's time for tea. > The poor little child is being taught a racist ditty by her perverted > racist father, he said. > Mr Irving replied: I am not a racist. > The historian and author of Hitler's War is suing Prof Lipstadt and > Penguin Books for libel over a claim in her book, Denying the > Holocaust: The Growing Assault on Truth and Memory, that he is a > Holocaust denier who falsified history. The defendants deny libel. > Mr Irving, 62, who is representing himself, told the court that he had > employed coloured people and ethnic minorities and that Mr Rampton's > legal team did not employ one such person. But Mr Justice Gray, who > is hearing the trial without a jury, told Mr Irving the comment was > not helpful. > Mr Rampton went on to refer to speeches made by Mr Irving. > In September 1992, he told his audience: > For a transitional period I'd be prepared to accept that the BBC > should have a dinner-jacketed gentleman reading the important news to > us, followed by a lady reading all the less important news, followed > by Trevor McDonald giving us all the latest news about the muggings > and the drug busts . . . > Are you not appalled by that? Mr Rampton said. > Not in the least, replied Mr Irving. > Addressing a meeting of the National Alliance, a Right-wing > organisation in America in October 1995, Mr Irving referred to the > legend of the Holocaust, the court heard. > Asked why he had told the audience he found the Holocaust boring, Mr > Irving said: What other explanation is there for the fact that it's > all they [Jews] go on about now. > Referring to his suggestion that a survivor may have faked her > Auschwitz tattoo, Mr Irving said his comments were not anti-Semitic > but were critical of those Jewish survivors who turned their > suffering into profit. The case continues. No doubt one can find events to slander and demonize anyone, even people like Abraham the patriarch of the Jewish lineage. Abraham pimped his wife Sara to the Egyptians, and when she gave Egyptians V.D., Abraham got kicked out of Egypt, Abraham was so upset about this, as he had gone to Egypt penniless, and made a lot of money pimping his wife, that he circumcised himself, his 13 year old son, and the slave that he bought with his pimping money. Genesis 12 10 And there was a famine in the land: and Abram went down into Egypt to sojourn there; for the famine was grievous in the land. 11 And it came to pass, when he was come near to enter into Egypt, that he said unto Sarai his wife, Behold now, I know that thou art a fair woman to look upon: 12 Therefore it shall come to pass, when the Egyptians shall see thee, that they shall say, This is his wife: and they will kill me, but they will save thee alive. 13 Say, I pray thee, thou art my sister: that it may be well with me for thy sake; and my soul shall live because of thee. 14 And it came to pass, that, when Abram was come into Egypt, the Egyptians beheld the woman that she was very fair. 15 The princes also of Pharaoh saw her, and commended her before Pharaoh: and the woman was taken into Pharaoh's house. 16 And he entreated Abram well for her sake: and he had sheep, and oxen, and he asses, and menservants, and maidservants, and she asses, and camels. 17 And the LORD plagued Pharaoh and his house with great plagues because of Sarai Abram's wife. Genesis 17 24 And Abraham was ninety years old and nine, when he was circumcised in the flesh of his foreskin. 25 And Ishmael his son was thirteen years old, when he was circumcised in the flesh of his foreskin. 26 In the selfsame day was Abraham circumcised himself, and Ishmael his son. 27 And all the men of his house, born in the house, and bought with money of the stranger, were circumcised with him. The Roman authors tell us that Moses and his gang did not leave Egypt on their own, but were also kicked out for giving Egyptians V.D. -- Tom was incapable of dealing with the following posting: Oh dear Tom, you expose your immense ignorance once more. Slander is any false or defamatory words SPOKEN about a person. You probably mean libel which is WRITING a defamatory or injurious statement about a person. Defamatory means injurious to a person's good name or reputation. Legally any statement which is true cannot be defamatory. Her is a resume of the judge's findings regarding Irving: Judge Gray found that Irving had for his own ideological reasons persistently and deliberately misrepresented and manipulated historical evidence in order to portray Hitler in an unwarrantedly favourable light particularly in his treatment of the Jews. Irving had significantly misrepresented, misconstrued, omitted, mistranslated, misread and applied double standards to the historical evidence in order to achieve his ideological presentation of history. Judge Gray also found that Irving was an active Holocaust denier; that he is anti-semitic and racist, and that he associates with right- wing extremists who promote neo-Nazism. No reasonable person (this category does not include you) could then assert that I have either been untruthful or have injured Irving's reputation. To demonize means to make into a demon (an evil spirit or devil). I have merely shown the truth about Irving. If you see anything demonic in that true account you are judging Irving and his actions. I agree with that judgement, by the way. === Subject: Re: resolution AP-Reals and AP-adics are all Rational numbers and a division matrix yields Irrationals #498 new book 2nd edition: New True Mathematics posting-account=kZanLQoAAABvNhBbAlX1SsCxeprjdiHJ AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.59 Safari/525.19,gzip(gfe),gzip(gfe) > Now there is a assumption I am leaning on, but need to prove it. > Notice the Continued-Fractions of pi and e > pi = 3 + 1/(7 +1)/(15 + 1)/(1 + 1)/292 +... > You notation is a little confusing. I would write: > pi = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ... > for > pi = 3 + 1 > > 7 + 1 > > 1 + 1 > > 15 + 1 > > 292 + ... > e = 2 + 1/(1 +1)/(2 + 1)/(1 + 1)/(1 + 1)/4 +... > Those use all integer values. > It is easily provable that all real number, whether rational or > irrational, can be expressed as continued fractions using only > integers. Rational numbers, when expressed as continued fractions, > will have a finite number of terms. Irrational numbers will have an > infinite number of terms. > Old Math starts with the positive-integers and then builds up to the > Continued-Fraction as covering all the Reals. I start not with positive-integers. I start with AP-Reals, and want to > do a Rational program on them. Then I want to do a Continued-Fraction > program on them. A week ago, I thought this was clear to me. Today it is all muddy. AP-Reals are All Possible Digit Arrangements and there is a smallest > of these Positive AP-Reals as 0d000...0001 I have FrontView and BackView, which Old Reals never had. I do not know whether these AP-Reals have any irrational number > amoung them. For the past years, I thought that All Possible Digit Arrangements > would > include irrational numbers. Today I am not so sure. - Hide quoted text - > - Show quoted text - As a side note, the square roots of rational numbers will be either > rational or will be irrational with a continued fraction in whcih the > integers in the denominators will repeat cyclically. > But in the construction of AP-Reals-Rationals-Irrationals > where we start with the AP-Reals as a starting set, and > construct AP-Reals-Rationals as a larger set and a huge > matrix of every AP-Real possible combinations as numerators > and denominators. So the Rationals in AP-Reals-Rationals are > a larger set than the AP-Reals themselves. > Continued fractions require integer division. > The operation of division is not defined for matrices. There maybe room here for a definition of transcendental number - Hide quoted text - > - Show quoted text - So, if you are math savvy, you can anticipate my next question. > Is the matrix of AP-Reals-Rationals-Irrationals a larger set than > that of Continued Fractions that use only integers? > Non. Every real number can be expressed as a continued fraction. > Think of the proof as an exercise in converting from decimal > representation into continued fraction representation. > You see, I was assuming that using fractions themselves is > superfluous as the numbers in the Continued-Fractions. > ??? > If my assumption is wrong and that there are more numbers > than using only integers in Continued-Fractions, then I have > to reconsider the idea of transcendental numbers. > No. Long a go I constructed a spreadsheet (originally in Lotus 1-2-3, > now in Excel) that will calculate the continued fraction > representation of any number input to the limit of the precision of > the computer. As a side exercise, I was able to simultaneously > calculate the precision of the representation and the equivalent ratio > of integers. For example, the continued fraction approximation of pi > given above can also be represented as a sequence of integer ratios: > pi: 3, 22/7, 25/8, 355/113, ... > Interestingly, the precision is related to the integers A and B in the > rational representation > x ~= A/B > in that the error e <= 1/(A*B) > so the fractional error of representing pi as 355/113 is less than 1/ > (355/113) > Already, I know that the AP-Reals-Rationals-Irrationals have > numbers such as 0d000...0001/0d000...0002 which is not an > Old Real, not an Old Rational of Old Reals. > I have never seena definition of AP-Reals-Rationals-Irrationals. I > know that the set of all real numbers is the union of the set of all > rational numbers and the set of all irrational numbers, but the AP > confuses me. Is this some sort of vanity label, Archie? Not vanity. I put the Positive Integers as Infinite Integers with a > BackView and FrontView. So that 9999...9999 is a positive integer > and 7777....2222 another positive integer. And I construct a matrix > of all these positive integers as All Possible Digit Arrangements. I > call > them the Natural Numbers. I define the AP-Reals as All Possible Digit Arrangements and tack on a > decimal point. Prior to today, I believed these two sets had irrational numbers > included > within them. Pi for example would be as an integer 314159...120 And as an AP-Real > would be 3d14159......120 Its last three digits would be 120 to > account > for Regular Polyhedra division. Basically, I do two things differently from Old Math. I say the > Naturals are > Infinite-Integers and I tack on a FrontView with BackView. So other > than > that, the same thing as the Old Math. So I have two new features--- Infinite Integers and they have > FrontView > with BackView. I call them AP-adics. By a simple change in definition > the AP-Reals are produced. The difference between Old Reals and AP-Reals is that AP-Reals have > a FrontView with BackView. So if I use that number in a Continued-Fraction such as this: > 2 + 1/(0d000...0001/0d000...0002 +1)/(0d000...0001/0d000...0002 + > 1)/... > First you must define AP-Reals-Rationals-Irrationals. Then you must > defin *division* by AP-Reals-Rationals-Irrationals. > Tom Davidson > Richmond, VA I suppose I need to define what a Rational Integer is versus an > Irrational > Integer for AP-adics. Here is a list of all AP-adics from 0 to 100 000...0100 > . > . > . > 0000....0001 > 0000....0000 Now the list of all AP-adics below the South Pole is: > 9999....9999 to 000...0000 Now let me define an Irrational AP-adic as a fraction of any two given > AP-adics. Let me define a Rational AP-adic as a positive-integer. So that 1 and 2 are Rational AP-adics and 1/2 is an Irrational AP-adic Now, let me transfer to AP-Reals and a AP-Real of 0d000...0001 and > 0d000...0002 is a Rational-AP-Real, but 0d000...0001/0d000...0002 > is a point that is between 0 and 0d000...0001 and is an Irrational AP- > Real. So when I start out, Tom Davidson with the AP-Reals what they are > is all the Old Reals Rationals. The Old Real of 0.5 is the AP-Real-Rational of 0d500...000 But the AP-Reals-Rationals has a number that the Old Reals never had > as a rational number, namely 0d5000...00021 That is an AP-Reals-Rational number Now what happens when I divide 0d5000...000/ 0d500...0021 > What happens? Well, it is not a number known by the Old Math, or if they knew it, > it is an Irrational number to the Old Math. way back to some path of truth. I am going to define Irrational AP-adic as a division of two Rational > AP-adics. > And define an AP-Real as all Rational numbers and when I do a matrix > of All AP-Reals of All Possible Numerators and Denominators, those are > Irrational > AP-Reals. And for the finale' Tom, I can use the Continued-Fraction on the AP- > adics and the > AP-Reals, and from the Continued-Fraction I receive transcendental > numbers Let me give an example on AP-adics: We have pi in AP-adics as represented by: 3H14159....120 since pi has to satisfy regular-polyhedra and so its > last three > digits are 120 Now that number is the South Pole after a complete second transit > around the > globe and is 14% on the way away from the South Pole. That number is an AP-adic-Rational Number But what if I were to divide it as such 3H14159....120/3333....333 > then that would be a AP-adic-Irrational number And lastly, what if I used 3H14159..... and used 2H71828.... (which by > the > way is 71% past the North Pole enroute to the South Pole after one > circum > navigation around the globe). Where I used them in a Continued-Fraction 3H14... + 1 > > 2H71.... + 1 > > 2H71.... + 1 > > 15 + 1 > > 292 + ... And thus, I come up with a number that exists and can be called what?? > Called transcendental?? Summary: AP-adics are different from Naturals in that they are > infinite, > and possessing a FrontView with BackView. AP-Reals are the same > as Old Reals except they have a FrontView with BackView. > The Rationals in AP-Reals and AP-adics are simply the set as given. > The Irrational AP-Reals and Irrational AP-adics are matrices of all > possible combinations of numerators and denominators. Finally, when > we do a Continued-Fraction format on the AP-Reals and AP-adics > we come up with a new class of numbers which the Old Math would > likely call transcendental numbers Archimedes Plutoniumwww.iw.net/~a plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies yes 1/(x+y) partial fraction decomposition does throw a lot of people... === Subject: A090934 : More terms posting-account=rKEIpgoAAAAG35JYzUWw7gjKqLVQ2Xvt Gecko/2009032609 YFF3 Firefox/3.0.8,gzip(gfe),gzip(gfe) A090934 Primes such that least significant digit swapped with all other digits yields primes. First 150 terms: http : // zak08.livejournal.com/12478.html More terms? === Subject: Re: looking for a family of functions >I am looking for a family of functions with the following properties: Find a set of functions f_1(x), f_2(x), ..., f_n(x) that map from >one set, x in X, to another (I don't really want to specify that set >right now). The composition of arbitrary subsets of these functions acting on x >produces the same result as the outermost function in the composition >acting on x. For example: f_i(x) = f_i(f_j(x)) = f_i(f_j(f_k(...))) (i,j,k in some arbitrary index set) f_i(x) = 0 or f_i(x) = x work, but I looking for something a little >more interesting. To generalize to vector-valued functions f_i(x) = f_i(f_j(f_k(...)),f_l(...),...) Let us assume the apparently weaker f (f (x)) = f (x) for all i<>j [1] i j i Equation [1] says nothing if there is only one function (n=1), so let us also assume that there are at least two functions (n>1). For any point x in X, let P_i(x) be the equivalence class of x induced by the function f_i. That is, P (x) = { y : f (y) = f (x) } [2] i i i Obviously, x is in P_i(x) for all i. Furthermore, we have f (P (x)) = f (f (P (x))) = f (f (x)) = f (x) [3] j i j i i j i j Equation [3] simply says that P_i(x) is contained in P_j(x). Since i and j were arbitrary, P_j(x) is also contained in P_i(x). Thus, P_i(x) = P_j(x) for all i, j, and x. The multiple composition relation follows after we show the following Lemma ----- Suppose we have [1] and there are at least 2 functions. Then f (f (x)) = f (x) for all x and i [4] i i i Proof ----- Equation [1] says that for i<>j f (f (x)) = f (x) j i j This means that f_i(x) is in P_j(x), and since P_i(x) = P_j(x), we also see that f_i(x) is in P_i(x), that is, f (f (x)) = f (x) i i i QED Corollary --------- The fixed point set of f_i equals the range of f_i for all i. Proof ----- Equation [4] says that the range of f_i is contained in the fixed point set of f_i. Since the fixed point set of any function must be contained in its range, the fixed point set of f_i equals the range of f_i. QED Therefore, if we assume there are at least 2 functions (n>1), the apparently weaker statement [1] implies [4] and by induction, both imply the full composition relation. To create a family of functions that satisfies the composition rules specified above, first choose a partition of X. The parts of this partition will become the equivalence classes induced by functions in the family. Each function in the family corresponds to a choice of one element from each part of the partition. The results above show that all such families of functions are generated in this fashion. This is simply a justification of what Robert Israel has already said. Rob Johnson take out the trash before replying === Subject: Re: Fibonacci #'s in a 3D Cartisain coordinate system. An interesting addendum to my sequence by Sloane and Conway in OEIS. Do as a search in OEIS using the header below. Fibonacci numbers in a 3d coordinate system. Dan === Subject: Re: Fibonacci #'s in a 3D Cartisain coordinate system. <31078456.86144.1241959376569.JavaMail.jakarta@nitrogen.mathforum.org An interesting addendum to my sequence by Sloane and Conway in OEIS. Do as a search in OEIS using the header below. Fibonacci numbers in a 3d coordinate system. Dan Your is junk and you should seek to have it removed from OEIS. 1. The quality of the entry is poor: a. It has several misspelled words: Cartesain s.b. Cartesian, compliment s.b. complement alogrithm s.b. algorithm b. The program in Basic is a sorry obfuscated pile of bad variable names, unnecessary variables, and unnecessary code. c. The stuff about F_{3k} is badly stated d. No references, links, or formula are given. 2. The entry is not useful: a. When i>2, the sequence is S_i = (-1)^j * (F_i - S_{i-3}) with j = 0 if i mod 6 in {0,1,2}, else j = 1. I estimate the likelihood of that being a search target as zero. b. It doesn't provide any mathematical insight, even if someone's search of OEIS somehow arrived at it. Thus, your is junk and you should seek to have it removed from OEIS. -- jiw === Subject: Re: Volume's energy character matches a curve derived from Nature's basic constants Hi Uncle I see you are still blowing hard on everything and anything. MAYBE if you ever did anything Original, your comments would mean something besides sour grapes. All I discovered was that IF e & P^3 are connected via a straight line, THEN the line passes thru pi which is pi also. I did not claim any more than that. You on the other hand, fart claims out of your big ass hourly. I'll bet you think the Planc length physically exists. Your science guardianship borders on the hallucinogenic at times. -- Yours truly RD email mr.computer@pobox.com Volume's energy character matches a curve derived from Nature's basic > constants. consistent? > JIDSLOPE Abstract: Nature's mathematical constants form a straight line whose > slope is the same as the Rydberg physical constant.
The Five points are: (-1,-5/4), (pi/2,pi/2), (P^2,e), (3,pi) and (4,P^3). >[snip crap] 1) wrong > 2) idiot Given any two irrational numbers 'x' and 'y' it is always possible to >find integers j, k, m, n such that |(j)(x^m) - (k)(y^n)| < epsilon, >where epsilon is arbitrarily small. One should not be impressed by >such a relationship since one could find an arbitrarily large number >of relationships as good or better by picking any other irrational >number, like the Napierian base 'e', Euler's constant gamma, the >Golden Ratio, any irrational square root, etc. (pi)^4 + (pi)^5 = e^6 is wrong. >31, 331, 3331... are primes is wrong. >n^2 + n + 41 generates primes for n = 1,2,3... is wrong. >(3,472,073)^7 + (4,627,011)^7 = (4,710,868)^7 is wrong. It makes no difference how close they are, they are not exact. The >last example is good to better than 10^(-21) relative. It is wrong >and Fermat's last theorem is correct. idiot Even an idiot knows (3,472,073)^7 + (4,627,011)^7 = (4,710,868)^7 is >wrong. Don't calculate the front end, idiot, simply cycle the >rightmost digits and add. idiot === Subject: Re: Property of Algebraically closed fields > It might be illuminating and simpler to consider > the corresponding question for integrally closed > domains. Why so? Instinct would tell me that this would be even more complex. Suppose R1 is an integrally closed domain with > field of quotients F1 contained in K (a big > field as before), while R2 is an integrally > closed domains with field of quotients F2, > also contained in K. > Here you do not necessarily require F1 and F2 to be algebraically closed? > Let R3 be the smallest combined overring of > R1 and R2 that K contains. Is R3 necessarily > integrally closed? > If you did not make any specific requirement of F1 or F2 to be algebraically closed.. then the answer is no (Take R1 and R2 to be F1 itself and K to be its algebraic closure).. otherwise.. hmm.. Maybe we could make a further simplification of the problem by assuming that R1 and R2 are both valuation rings > Let's consider a concrete version of this > along the lines that Arturo poses. Let > R1 be the integral closure of Z[X] and let > R2 be the integral closure of Z[Y]. So you are in fact assuming that F1 and F2 arent algebraically closed.. >Then > we ask whether (X+Y)^(1/2) is in R3, i.e. > is it expressable as a polynomial in terms > of values integral over either Z[X] or Z[Y]. > I really do not see how this will give me an idea for a counterexample for the problem. Though I do see the point of Arturo.. Its easier to work out a finite extension of C (complex numbers) by one indeterminate element and consider compositum of two algebraically closed fields, I believe that would make the easiest possible counterexample. But Im not that good to imagine how algebraic closure of C(x1) and C(x2) and their compositum would look like .. do we know this? My thoughts are that the counterexample or proof would not be trivial. But maybe not. There is a work by Abhyankar on the compositum of two algebraically closed subfields of a field and I would probably first look at that.. but unfortunately I have no access to any decent library. It does suck when somethings arent electronically avaialble, maybe someone who has a free time could take a look at it and post here if in his work Abhyankar does provide a counterexample to this problem? I would be very thankful. Otherwise I might consider emailing him (though I'm not sure he would answer emails). Jose Capco === Subject: Re: Property of Algebraically closed fields Ok guys.. I got lucky and somebody lent me his jstor account so I could have a look at this work of Abhyankar -. By the way, interestingly this is his work 2 years after graduating PhD from Harvard. Interestingly, this question is exactly the question being asked in his paper.. and according to him the question was first propsed by Prof. Igusa (I know Igusa from his books on automorphic forms). Anyway getting back to the original topic. I didnt have time to read it exensively, but the counterexample uses exactly what Arturo pointed out. It uses the compositum of k(x) and k(y) for some algebraically closed field k. I will give a further report once I read this in full detail later in the week. Jose Capco === Subject: Re: Property of Algebraically closed fields <28309136.86874.1241986402218.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009042513 Ubuntu/8.04 (hardy) Firefox/3.0.10,gzip(gfe),gzip(gfe) > Ok guys.. I got lucky and somebody lent me his jstor account so I could have a look at this work of Abhyankar -. By the way, interestingly this is his work 2 years after graduating PhD from Harvard. Interestingly, this question is exactly the question being asked in his paper.. and according to him the question was first propsed by Prof. Igusa (I know Igusa from his books on automorphic forms). Anyway getting back to the original topic. I didnt have time to read it exensively, but the counterexample uses exactly what Arturo pointed out. It uses the compositum of k(x) and k(y) for some algebraically closed field k. I will give a further report once I read this in full detail later in the week. Nice to know my intuition was pointing in the right direction... Look forward to hearing the full report. -- Arturo Magidin === Subject: higher dimensional matrices posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009032712 Ubuntu/8.10 (intrepid) Firefox/3.0.8,gzip(gfe),gzip(gfe) does a theory on higher dimensional matrices exist? I am pretty sure that it does but I cannot find anything about it. What's the right keyword to search for? For what are higher dimensional matrices good for? S. === Subject: Re: higher dimensional matrices > does a theory on higher dimensional matrices exist? I am pretty sure > that it does but I cannot find anything about it. What's the right > keyword to search for? > For what are higher dimensional matrices good for? Maybe it is tensor theory? It has many usages in physics, starting with (seemingly) simple theory of mechanics of moving a solid body without external forces. http://en.wikipedia.org/wiki/Tensor I'm like the original poster is also intrigued whether there is multi- dimensional matrix theory besides tensor theory. === Subject: Re: higher dimensional matrices posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009032712 Ubuntu/8.10 (intrepid) Firefox/3.0.8,gzip(gfe),gzip(gfe) does a theory on higher dimensional matrices exist? I am pretty sure > that it does but I cannot find anything about it. What's the right > keyword to search for? > For what are higher dimensional matrices good for? Maybe it is tensor theory? It has many usages in physics, starting > with (seemingly) simple theory of mechanics of moving a solid body > without external forces. http://en.wikipedia.org/wiki/Tensor I'm like the original poster is also intrigued whether there is multi- > dimensional matrix theory besides tensor theory. physicists mean when they speak about tensors. It seems to me that a tensor is something different in mathematics than it is in physics, i.e. some universal object (http://en.wikipedia.org/wiki/ Tensor product of R-algebras). Can someone provide me a text which introduces tensors as a generalization of scalars, vectors, matrices in a strict mathematical context? S. === Subject: Re: higher dimensional matrices posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc10 Firefox/3.0.10,gzip(gfe),gzip(gfe) > does a theory on higher dimensional matrices exist? I am pretty sure > that it does but I cannot find anything about it. What's the right > keyword to search for? > For what are higher dimensional matrices good for? Maybe it is tensor theory? It has many usages in physics, starting > with (seemingly) simple theory of mechanics of moving a solid body > without external forces. http://en.wikipedia.org/wiki/Tensor I'm like the original poster is also intrigued whether there is multi- > dimensional matrix theory besides tensor theory. physicists mean when they speak about tensors. It seems to me that a > tensor is something different in mathematics than it is in physics, > i.e. some universal object (http://en.wikipedia.org/wiki/ > Tensor product of R-algebras). Can someone provide me a text which > introduces tensors as a generalization of scalars, vectors, matrices > in a strict mathematical context? Physicists identify a tensor with the array of its coefficients with respect to a basis. At the same time, they do not consider every array of scalars to be a tensor unless it changes in the correct way with respect to change of variables. This is quite correct, although much more clumsier that the intrinsic approach mathematicians tend to favor---at least when these mathematicans are not doing actual computations! -- m === Subject: Re: higher dimensional matrices > does a theory on higher dimensional matrices exist? > I am pretty sure that it does but I cannot find anything > about it. What's the right keyword to search for? > For what are higher dimensional matrices good for? > Maybe it is tensor theory? It has many usages in physics, > starting with (seemingly) simple theory of mechanics of > moving a solid body without external forces. http://en.wikipedia.org/wiki/Tensor I'm like the original poster is also intrigued whether > there is multi-dimensional matrix theory besides tensor theory. The key is to search for a higher dimensional analog of determinants, since until the 1930s or 1940s (?), determinants were the more basic object of study. hyper determinants. Dave L. Renfro === Subject: Re: higher dimensional matrices <30424450.86424.1241968637168.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > does a theory on higher dimensional matrices exist? > I am pretty sure that it does but I cannot find anything > about it. What's the right keyword to search for? > For what are higher dimensional matrices good for? > Maybe it is tensor theory? It has many usages in physics, > starting with (seemingly) simple theory of mechanics of > moving a solid body without external forces. http://en.wikipedia.org/wiki/Tensor I'm like the original poster is also intrigued whether > there is multi-dimensional matrix theory besides tensor theory. The key is to search for a higher dimensional analog > of determinants, since until the 1930s or 1940s (?), > determinants were the more basic object of study. hyper determinants. Dave L. Renfro The rather subtle problem of coming up with a good analogue of determinants for higher-dimensional matrices has a more or less correct answer nowadays. See Discriminants, Resultants, and Multidimensional Determinants by Israel M. Gelfand, Mikhail Kapranov, Andrei Zelevinsky. -- m === Subject: Why does hydrogen congregate at the right amount to form stars? Masses of hydrogen form into stars under its own gravity. Why isn't there on occasion too much or too little hydrogen? Why aren't there as many black holes as stars? Why aren't there trillions of big globules of hydrogen too small to start fusion? Final teaser question. If our sun had one extra molecule of hydrogen would our history be any different? clue: would any extra photons be given off or would the change in gravity have any effect on Earth's orbit? It's a butterly flaps it's wings chaos theory question. Herc -- http://twitter.com/freetruman === Subject: Re: Why does hydrogen congregate at the right amount to form stars? > Masses of hydrogen form into stars under its own gravity. > Why isn't there on occasion too much or too little hydrogen? When enough accumulates to ignite, it does, and that creates a solar wind effect making it difficult to accumulate any more hydrogen molecules. By that time they're large enough to suck in matter with a size/density ratio that overcomes the solar wind. Startup size is self-regulating. > Why aren't there as many black holes as stars? > Why aren't there trillions of big globules of hydrogen too small to start fusion? Could you see them if there were? Also, time is on the side of growth and ignition. > Final teaser question. If our sun had one extra molecule of hydrogen would > our history be any different? clue: would any extra photons be given off or > would the change in gravity have any effect on Earth's orbit? It's a butterly > flaps it's wings chaos theory question. That would be one hell of a butterfly. === Subject: Re: Why does hydrogen congregate at the right amount to form stars? > Final teaser question. If our sun had one extra molecule of hydrogen would > our history be any different? clue: would any extra photons be given off or > would the change in gravity have any effect on Earth's orbit? It's a butterly > flaps it's wings chaos theory question. > That would be one hell of a butterfly. > If you changed one thought in your mind one day.... Within minutes your train of thought would be entirely different. You would be in a different position in a different location doing something different. Within hours your interactions with others would be different and they would all be altered too. Every car on the road that comes within sight of people you've been in contact with would be slightly affected. Within days everybody in the city would be doing something different than they would have been. These changed people would migrate to other cities and within weeks the events of the entire population of the Earth would be altered. Different positions, different thoughts, different conversations, different news headlines, different sport outcomes, everything different! And a drop of rain could set it off. Herc === Subject: Re: Why does hydrogen congregate at the right amount to form stars? Louis de Broglie The Nobel Prize in Physics 1929 http://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-bio.html WAVE MECHANICS Prince Louis de Broglie http://www.davis-inc.com/physics/ -- Ahmed Ouahi, Architect Jack Sprat kirjoitti viestiss.8a:45e65$4a070e1c$cdd085b5$24316@DIALUPUSA.NET... > Masses of hydrogen form into stars under its own gravity. > Why isn't there on occasion too much or too little hydrogen? When enough accumulates to ignite, it does, and that creates a > solar wind effect making it difficult to accumulate any more > hydrogen molecules. By that time they're large enough to suck > in matter with a size/density ratio that overcomes the solar > wind. Startup size is self-regulating. > Why aren't there as many black holes as stars? > Why aren't there trillions of big globules of hydrogen too small to start > fusion? Could you see them if there were? Also, time is on the side of > growth and ignition. > Final teaser question. If our sun had one extra molecule of hydrogen > would > our history be any different? clue: would any extra photons be given off > or > would the change in gravity have any effect on Earth's orbit? It's a > butterly > flaps it's wings chaos theory question. > That would be one hell of a butterfly. > === Subject: Re: Why does hydrogen congregate at the right amount to form stars? posting-account=qKxGxgkAAADAPfYVCc-ZQkIzl0senr2M .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 1.1.4322; Zune 2.5),gzip(gfe),gzip(gfe) > Masses of hydrogen form into stars under its own gravity. > Why isn't there on occasion too much or too little hydrogen? There usually is. > Why aren't there as many black holes as stars? It takes more mass than one average star to make a black hole. > Why aren't there trillions of big globules of hydrogen too small to start fusion? There are. They are quite common. We call them failed stars and they are usually found in the gravitational neighborhood of something more massive - i.e. successful stars. Side note, if the globules are so small that their own gravitation cannot prevent the evaporation of hydrogen out of the gravity well, then they evaporate and become gas clouds, cooling down in the process. > Final teaser question. If our sun had one extra molecule of hydrogen would > our history be any different? How would you know? The question is overated, as are almost all hypothetical questions that don't educe testable answers. Tom Davidson Richmond, VA === Subject: Re: Why does hydrogen congregate at the right amount to form stars? > Final teaser question. If our sun had one extra molecule of hydrogen would > our history be any different? How would you know? The question is overated, as are almost all hypothetical questions that don't educe testable answers. Tom Davidson Richmond, VA I thought maybe after a trillion days of Earth spinning the accumulated change might alter the time of day by a trillionth of a second. Which would have an enormous impact on an alternate world. You don't require two alternate worlds just to test each hypothesis whether history is altered or not. If you mean physically_testable then your domain of knowledge must be very small. Herc === Subject: Re: Why does hydrogen congregate at the right amount to form stars? *plonk* Do not reply to this generic message, it was automatically generated; you have been kill-filed, either for being boringly stupid, repetitive, unfunny, ineducable, repeatedly posting politics, religion or off-topic subjects to a sci. newsgroup, attempting cheapskate free advertising for profit, because you are a troll, simply insane or any combination or permutation of the aforementioned reasons; any reply will go unread. Boringly stupid is the most common cause of kill-filing, but because this message is generic the other reasons have been included. You are left to decide which is most applicable to you. There is no appeal, I have despotic power over whom I will electronically admit into my home and you do not qualify as a reasonable person I would wish to converse with or even poke fun at. Some weirdoes are not kill- filed, they amuse me and I retain them for their entertainment value as I would any chicken with two heads, either one of which enables the dumb bird to scratch dirt, step back, look down, step forward to the same spot and repeat the process eternally. This should not trouble you, many of those plonked find it a blessing that they are not required to think and can persist in their bigotry or crackpot theories without challenge. You have the right to free speech, I have the right not to listen. The kill-file will be cleared annually with spring cleaning or whenever I purchase a new computer or hard drive. I hope you find this explanation is satisfactory but even if you don't, damnly my frank, I don't give a dear. Have a nice day. > Final teaser question. If our sun had one extra molecule of hydrogen > would > our history be any different? How would you know? The question is overated, as are almost all > hypothetical questions that don't educe testable answers. Tom Davidson > Richmond, VA > I thought maybe after a trillion days of Earth spinning the accumulated > change might > alter the time of day by a trillionth of a second. Which would have an > enormous impact > on an alternate world. You don't require two alternate worlds just to > test each hypothesis > whether history is altered or not. If you mean physically_testable then > your domain of knowledge > must be very small. Herc === Subject: Re: Why does hydrogen congregate at the right amount to form stars? > Masses of hydrogen form into stars under its own gravity. > Why isn't there on occasion too much or too little hydrogen? > Why aren't there as many black holes as stars? > Why aren't there trillions of big globules of hydrogen too small to start fusion? Final teaser question. If our sun had one extra molecule of hydrogen would > our history be any different? clue: would any extra photons be given off or > would the change in gravity have any effect on Earth's orbit? It's a butterly > flaps it's wings chaos theory question. Herc Google is your friend. === Subject: Re: Why does hydrogen congregate at the right amount to form stars? > Masses of hydrogen form into stars under its own gravity. > Why isn't there on occasion too much or too little hydrogen? > Why aren't there as many black holes as stars? > Why aren't there trillions of big globules of hydrogen too small to > start fusion? > Final teaser question. If our sun had one extra molecule of hydrogen > would > our history be any different? clue: would any extra photons be given > off or > would the change in gravity have any effect on Earth's orbit? It's a > butterly > flaps it's wings chaos theory question. > Herc > Google is your friend. > Would it were so. === Subject: Question about Complex Made Simple posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) Hi all I'm reading Chapter 22 of Prof. Ullrich's book, and I am stuck on exercise 22.2: suppose that u_n is harmonic in the disc D = {z in C | | z| < 1} for each n in N, and that v_n is the harmonic conjugate of u_n (i.e. a harmonic function on D such that u_n + i*v_n is holomorphic), with v_n(0) = 0. Suppose further that u_n -> 0 uniformly on compact subsets of D. I need to show that v_n -> 0 uniformly on compact subsets of D. I expect I'm being dim, but I really have no idea how to go about this question. === Subject: Re: Question about Complex Made Simple posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Hi all I'm reading Chapter 22 of Prof. Ullrich's book, and I am stuck on > exercise 22.2: suppose that u n is harmonic in the disc D = {z in C | | > z| < 1} for each n in N, and that v n is the harmonic conjugate of u n > (i.e. a harmonic function on D such that u n + i*v n is holomorphic), > with v n(0) = 0. Suppose further that u n -> 0 uniformly on compact > subsets of D. I need to show that v n -> 0 uniformly on compact > subsets of D. Show that u n + i*v n converges to a holomorphic function uniformly on compact subsets of the disk. The limit has vanishing real part, so it is constant. -- m === Subject: Re: Question about Complex Made Simple posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) On 10 May, 19:22, Mariano Su.87rez-Alvarez Hi all I'm reading Chapter 22 of Prof. Ullrich's book, and I am stuck on > exercise 22.2: suppose that u n is harmonic in the disc D = {z in C | | > z| < 1} for each n in N, and that v n is the harmonic conjugate of u n > (i.e. a harmonic function on D such that u n + i*v n is holomorphic), > with v n(0) = 0. Suppose further that u n -> 0 uniformly on compact > subsets of D. I need to show that v n -> 0 uniformly on compact > subsets of D. Show that u n + i*v n converges to a holomorphic > function uniformly on compact subsets of the disk. Could you give me another hint? > The limit has vanishing real part, so it is constant. Also, a question for David: am I correct in thinking that every occurrence of $Omega cup D(0,r)$ in the proof of Lemma 23.0.0 should be $Omega cap D(0,r)$? === === Subject: Re: all matrices whose image contains a given vector >statement > and this is the set of matrices whose first k rows are linearly , > independent , since any such > (and only such) matrices allow a decomposition > DQ = [L* R , S ; O , T ] because the matrix D = [I;I], with I having dimensions n x n, has its >first n rows linearly independent, but it cannot solve any equations I assumed of course that column number >= row number, as you see from the derivation of the result. you should make clear the relation of dimensions of A, (and in your more advanced case, of course of the column number of B,C and this k. What is required: since your right hand side is arbitrary in the first k positions due to linearity and you require sovability for a basis in R^k, there must be an invertible subsystem of dimension k. In your case this is of course the first I. clearly now the column number of A cannot be less than k. Since on the other side you require also solvability of a further homogenous subsystem , there must, after only column operations, vanish the subsytem in A corresponding to the first k columns in the transformed system hence n = column number >= k you can handle this using the singular values decomposition of A: A = U [S;O] V' we can replace V'x by y getting [S;O] y = U'[(*****)';0] S is n by n diagonal but has also zeros on the diagonal if rank(A)of the form Dx = (*,,,,*,0,...0)'. Moreover, wouldn't the above >condition also hold true for any matrix Q, not just a column >permutation (say an orthogonal matrix, for example)? yes, you can use any invertible transformation on the right, but in the case you have in mind this does not help: > === Subject: solutions manual and Test Bank posting-account=ldzOOQoAAAALmEmlIRVd1wCu2DOhImIB CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank Solutions Manuals and Test Bank in Electronic (PDF)Format! 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But I'm not seeing why this is the case. An interval [0, 1] has measure 1. The rationals on this interval have measure 0 (and the set of the rationals in general). A given interval (a, b) has outer measure b - a. So it seems to me that any interval of all real numbers has measure > 0. I get that the rationals have measure 0 because each point can be thought of as a disjoint set, and each point can be contained in an interval < epsilon for any arbitrarily small epsilon. Between any two rationals there is an irrational number. But between any two irrationals there is a rational number. What makes the irrationals different? There are more of them? How does this make sense? === Subject: Re: Why do irrationals have measure 1 on [0, 1] and rationals have measure 0? > OK, this is a naive question. But I'm not seeing why this is the case. > An interval [0, 1] has measure 1. The rationals on this interval have > measure 0 (and the set of the rationals in general). A given interval > (a, b) has outer measure b - a. So it seems to me that any interval of > all real numbers has measure > 0. I get that the rationals have > measure 0 because each point can be thought of as a disjoint set, and > each point can be contained in an interval < epsilon for any > arbitrarily small epsilon. Between any two rationals there is an > irrational number. But between any two irrationals there is a rational number. What makes > the irrationals different? There are more of them? How does this > make sense? > For one thing, the rationals can be ennumerated (put into a list with a first, second, etc., so that all of them are accounted for) but the irrationals cannot (a secondary result of the Cantor diagonal theorem showing that the set of all binary infinite seqeunces cannot be ennumerated). Thus even though each is dense in the other, there are more irrationals than rationals. It can also be shown that the (countable) set of ratinoals in any interval has an open cover of arbitrarily small total measure. === Subject: Re: Why do irrationals have measure 1 on [0, 1] and rationals have measure 0? > OK, this is a naive question. But I'm not seeing why this is the case. > An interval [0, 1] has measure 1. The rationals on this interval have > measure 0 (and the set of the rationals in general). A given interval > (a, b) has outer measure b - a. So it seems to me that any interval of > all real numbers has measure > 0. I get that the rationals have > measure 0 because each point can be thought of as a disjoint set, and > each point can be contained in an interval < epsilon for any > arbitrarily small epsilon. Between any two rationals there is an > irrational number. But between any two irrationals there is a rational number. What makes > the irrationals different? There are more of them? How does this > make sense? The why-question in mathematics is usually answered by looking at and understanding proofs. There are more irrationals than rationals in the sense that we can make a one-to-one relation between the naturals ( {0,1,2,3,4,...} ) and the rationals, but we cannot make such a relation between the naturals and the irrationals. Google for: infinity cantor set theory diagonal Dirk Vdm === Subject: Re: Why do irrationals have measure 1 on [0, 1] and rationals have measure 0? posting-account=JVPKNAoAAADT8GA9RydVIuuyOWRYhdVD .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On May 10, 12:44pm, Dirk Van de moortel > OK, this is a naive question. But I'm not seeing why this is the case. > An interval [0, 1] has measure 1. The rationals on this interval have > measure 0 (and the set of the rationals in general). A given interval > (a, b) has outer measure b - a. So it seems to me that any interval of > all real numbers has measure > 0. I get that the rationals have > measure 0 because each point can be thought of as a disjoint set, and > each point can be contained in an interval < epsilon for any > arbitrarily small epsilon. Between any two rationals there is an > irrational number. But between any two irrationals there is a rational number. What makes > the irrationals different? There are more of them? How does this > make sense? The why-question in mathematics is usually answered by looking at > and understanding proofs. > There are more irrationals than rationals in the sense that we can > make a one-to-one relation between the naturals ( {0,1,2,3,4,...} ) > and the rationals, but we cannot make such a relation between the > naturals and the irrationals. > Google for: > infinity cantor set theory diagonal Dirk Vdm has measure 0? So the elements of the Cantor set cannot be put into one-to-one correspondence with the naturals, right? === Subject: Re: Why do irrationals have measure 1 on [0, 1] and rationals have measure 0? > On May 10, 12:44pm, Dirk Van de moortel > OK, this is a naive question. But I'm not seeing why this is the case. > An interval [0, 1] has measure 1. The rationals on this interval have > measure 0 (and the set of the rationals in general). A given interval > (a, b) has outer measure b - a. So it seems to me that any interval of > all real numbers has measure > 0. I get that the rationals have > measure 0 because each point can be thought of as a disjoint set, and > each point can be contained in an interval < epsilon for any > arbitrarily small epsilon. Between any two rationals there is an > irrational number. But between any two irrationals there is a rational number. What makes > the irrationals different? There are more of them? How does this > make sense? The why-question in mathematics is usually answered by looking at > and understanding proofs. > There are more irrationals than rationals in the sense that we can > make a one-to-one relation between the naturals ( {0,1,2,3,4,...} ) > and the rationals, but we cannot make such a relation between the > naturals and the irrationals. > Google for: > infinity cantor set theory diagonal Dirk Vdm has measure 0? So the elements of the Cantor set cannot be put into > one-to-one correspondence with the naturals, right? Right! === Subject: Re: Why do irrationals have measure 1 on [0, 1] and rationals have measure 0? > On May 10, 12:44pm, Dirk Van de moortel > OK, this is a naive question. But I'm not seeing why this is the case. > An interval [0, 1] has measure 1. The rationals on this interval have > measure 0 (and the set of the rationals in general). A given interval > (a, b) has outer measure b - a. So it seems to me that any interval of > all real numbers has measure > 0. I get that the rationals have > measure 0 because each point can be thought of as a disjoint set, and > each point can be contained in an interval < epsilon for any > arbitrarily small epsilon. Between any two rationals there is an > irrational number. But between any two irrationals there is a rational number. What makes > the irrationals different? There are more of them? How does this > make sense? The why-question in mathematics is usually answered by looking at > and understanding proofs. > There are more irrationals than rationals in the sense that we can > make a one-to-one relation between the naturals ( {0,1,2,3,4,...} ) > and the rationals, but we cannot make such a relation between the > naturals and the irrationals. > Google for: > infinity cantor set theory diagonal Dirk Vdm has measure 0? So the elements of the Cantor set cannot be put into > one-to-one correspondence with the naturals, right? Yes, true. Any countable set has measure 0. The Cantor set is a counterexample to the converse. That is, the proposition Any set of measure 0 must be countable is shown to be false by the existence of the Cantor set. === Subject: Re: Why do irrationals have measure 1 on [0, 1] and rationals have measure 0? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > On May 10, 12:44pm, Dirk Van de moortel OK, this is a naive question. But I'm not seeing why this is the case. > An interval [0, 1] has measure 1. The rationals on this interval have > measure 0 (and the set of the rationals in general). A given interval > (a, b) has outer measure b - a. So it seems to me that any interval of > all real numbers has measure > 0. I get that the rationals have > measure 0 because each point can be thought of as a disjoint set, and > each point can be contained in an interval < epsilon for any > arbitrarily small epsilon. Between any two rationals there is an > irrational number. But between any two irrationals there is a rational number. What makes > the irrationals different? There are more of them? How does this > make sense? The why-question in mathematics is usually answered by looking at > and understanding proofs. > There are more irrationals than rationals in the sense that we can > make a one-to-one relation between the naturals ( {0,1,2,3,4,...} ) > and the rationals, but we cannot make such a relation between the > naturals and the irrationals. > Google for: > infinity cantor set theory diagonal Dirk Vdm has measure 0? So the elements of the Cantor set cannot be put into > one-to-one correspondence with the naturals, right? Indeed. It is true that a countable set always have measure zero, but it is not true that all uncountable setshave positive measure. You need to know how the points are actually laid out in the line to know the measure. With the Cantor set, what happens is that the set has so many holes and theses holes are so big when compared with the set itself that the measure is zero. You can construct variations of the Cantor set (by taking away different intervals of varying width) to get sets which are of the same cardinal and of the same rough shape as the original Cantor set but which have positive measure. -- m === Subject: Re: Cantor's argument is erroneous > As we surely agree, there is no ordinary convention that the rules of > inference pertain only to formulas with only symbols mentioned in some > non-logical set of axioms. If Nam disputes that, then he's just wrong. > In so far as you and others have not been able to refute my specific > examples > at all (other than saying something like Shoenfield, Roger, etc... didn't > say that, or invoking off-the-topic non-FOL= logic frameworks) then > I'm correct and you and other opponents of mine are *not*. Also you (MoeBlee) should have realized that as far as FOL= *proof in a theory* > is concerned, *rules of inference don't pertain to just _any_ formula*! They pertain to any formula in the language being considered; the choice of language is not always made explicit, but simply saying you are using FOL= as a framework is not enough; to be precise, the language has to be made explicit as well. > Specifically, rules of inference pertain *only* to formulas that are > *theorems*. But since theorems are defined from axioms, it isn't much > an exaggeration to say rules of inference pertains to *axioms*. [And that's > not just (in your words) ordinary convention but it's the very heart of the > definition of proofs - in FOL=]. So you and others are not *just* disputing with me: you're disputing the > very fundamental notion of syntactical proofs in FOL=. Absolutely not, and you have already seen examples. Perhaps the best example comes when there are *no* (non-logical) axioms at all. Logic text books are full of examples asking students to show that certain statements are theorems of FOL=, with *no* axioms. (the language is implicitly or explicitly assumed to be such that the formla in question is well formed). e.g., if wotsit is a 1-place predicate, then (all x. not wotsit(x)) -> not (some y wotsit(y)) is provable in whatever system of FOL you want, from no non-logical axioms. You seem to be saying that without non-logical axioms, *nothing* is provable in FOL= -- that's just no so. < == > To discover the proper approach to mathematical logic, > we must therefore examine the methods of the mathematician. > (Shoenfield, Mathematical Logic) -- Alan Smaill === Subject: Re: NY Times math problem <12nb0554acbsf5dghh2ns000e4ce7dsd9n@4ax.com> posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; GTB6; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On May 9, 2:43pm, Archimedes' Lever agent is *near* the 180 degree point. He doesn't have to get him there > exactly. The rabbit does need to position himself exactly on the opposite side of the diameter from the agent if he expects to escape when the agent is running the fastest he can for the rabbit to escape, if both use optimal strategies. Assuming that the rabbit starts at the center and that the agent is running at full speed, the rabbit can remain on the diameter through the agent reach the furthest radius at which his angular rate equals that of the agent while the agent travels 90 degrees around the pond. Dave === Subject: Re: NY Times math problem <87hc012hno.fsf@temporary-address.org.uk> <4rmb05pr1gko1lr6p44cv9km8g3q05sfau@4ax.com> +M[5[U[QT7xFN%^gR=tuJw%TXXR'Fp~W;(T1(739R%m0Yyyv*gkGoPA.$b,D.w:z+<'=-lV T?6 {T?=R^:W5g|E2#EhjKCa+nt:4b}dU7GYB*HBxn&Td$@f%.kl^:7X8rQWd[NTcPu6nkisze/ Q;8 9Z{peQF,w)7UjV$c|RO/mQW/NMgWfr5*$-Z%u46/00mx-,R'fLPe.)^ then if the agent always runs toward the aim point then the rabbit > can escape (even if the agent is very fast). But this assumes a > stupid agent >Yes it does, which is exactly why I was arguing that it was a poor >strategy for the agent to employ. >- Tim The rabbit will ALWAYS use his peripheral vision to determine the > agent's position, and will always swim away from that attempt at capture. They have over 270 degrees of vision without even turning their head. the dumb bunny will never leave the pool. === Subject: Re: NY Times math problem <3A3Nl.39172$qa.25218@bignews4.bellsouth.net> posting-account=msV4aQkAAACFdekrjeDyuMHhzZGN7wbC 3.22; GTB6; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; InfoPath.2; IEMB3),gzip(gfe),gzip(gfe) > The rabbit does not know anything except whether or not it is rotating > with > a radial to the agent...and if it is on the other side of the radius. > If the rabbit also knows the direction to the nearest shore. > adopt the following strategy (which does not involve > calculation): Step 1. a: Keep rotating with a radial to the agent > b: if not using maximum speed for a: > turn toward the nearest shore until > using maximum speed. > c: continue until not approaching the nearest > shore Step 2. a: Swim directly toward the nearest shore > at maximum speed. This will allow the rabbit to escape given any > agent strategy if the agent's top > speed is less than (pi+1) times the rabbit's > (a slightly more complex strategy for step 2, also > involving no calculation, can improve this a > little). > Okay the rabbit's name is Duck... > The speeds are fixed but since the agent can stop maybe I should allow > Duck to slow down. But when they sprint just say that both increase speed > at the same percentage so that it's not necessary to allow for increased > speed of a sprint...over their given rates. > But I'm not allowing Duck to know where 1/4 radius distance is as some > point in the water. I'm only allowing Duck to know whether or not he is > rotating with the agent...and that finds the break point. I think we should stay with the fixed speeds... We just find them in motion. The agent can't stop but can reverse > direction. And don't worry about sprint speeds as both speeds could > increase at the same rate... We just find them in motion... And allowing the agent to reverse direction is just to eliminate the > with the agent by spiraling outward but must also maneuver to be on the > point on the other side of the radius from the agent.- Hide quoted text - - Show quoted text - Why are we constraining outselves to the rabbit moving in a spiral or along the radius of a circle? Could there not be a solution where the rabbit moves in an elliptical path, allowing the agent to gain and lose ground relative to the rabbit until the rabbit finds itself opposite the agent, but closer to the edge than a circular path would bring it? --riverman === Subject: Re: NY Times math problem > The rabbit does not know anything except whether or not it is rotating > with > a radial to the agent...and if it is on the other side of the radius. > If the rabbit also knows the direction to the nearest shore. > adopt the following strategy (which does not involve > calculation): Step 1. a: Keep rotating with a radial to the agent > b: if not using maximum speed for a: > turn toward the nearest shore until > using maximum speed. > c: continue until not approaching the nearest > shore Step 2. a: Swim directly toward the nearest shore > at maximum speed. This will allow the rabbit to escape given any > agent strategy if the agent's top > speed is less than (pi+1) times the rabbit's > (a slightly more complex strategy for step 2, also > involving no calculation, can improve this a > little). > Okay the rabbit's name is Duck... > The speeds are fixed but since the agent can stop maybe I should allow > Duck to slow down. But when they sprint just say that both increase speed > at the same percentage so that it's not necessary to allow for increased > speed of a sprint...over their given rates. > But I'm not allowing Duck to know where 1/4 radius distance is as some > point in the water. I'm only allowing Duck to know whether or not he is > rotating with the agent...and that finds the break point. I think we should stay with the fixed speeds... We just find them in motion. The agent can't stop but can reverse > direction. And don't worry about sprint speeds as both speeds could > increase at the same rate... We just find them in motion... And allowing the agent to reverse direction is just to eliminate the > with the agent by spiraling outward but must also maneuver to be on the > point on the other side of the radius from the agent.- Hide quoted text - - Show quoted text - Why are we constraining outselves to the rabbit moving in a spiral or > along the radius of a circle? Could there not be a solution where the > rabbit moves in an elliptical path, allowing the agent to gain and > lose ground relative to the rabbit until the rabbit finds itself > opposite the agent, but closer to the edge than a circular path would > bring it? There is no rabbit/duck elliptical strategy which is as good as the one being questioned when the agent pursues an optimal strategy. --riverman === Subject: Re: NY Times math problem <3A3Nl.39172$qa.25218@bignews4.bellsouth.net> posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; GTB6; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > The rabbit does not know anything except whether or not it is rotating > with > a radial to the agent...and if it is on the other side of the radius. > If the rabbit also knows the direction to the nearest shore. > adopt the following strategy (which does not involve > calculation): Step 1. a: Keep rotating with a radial to the agent > b: if not using maximum speed for a: > turn toward the nearest shore until > using maximum speed. > c: continue until not approaching the nearest > shore Step 2. a: Swim directly toward the nearest shore > at maximum speed. This will allow the rabbit to escape given any > agent strategy if the agent's top > speed is less than (pi+1) times the rabbit's > (a slightly more complex strategy for step 2, also > involving no calculation, can improve this a > little). > Okay the rabbit's name is Duck... > The speeds are fixed but since the agent can stop maybe I should allow > Duck to slow down. But when they sprint just say that both increase speed > at the same percentage so that it's not necessary to allow for increased > speed of a sprint...over their given rates. > But I'm not allowing Duck to know where 1/4 radius distance is as some > point in the water. I'm only allowing Duck to know whether or not he is > rotating with the agent...and that finds the break point. I think we should stay with the fixed speeds... We just find them in motion. The agent can't stop but can reverse > direction. And don't worry about sprint speeds as both speeds could > increase at the same rate... We just find them in motion... And allowing the agent to reverse direction is just to eliminate the > with the agent by spiraling outward but must also maneuver to be on the > point on the other side of the radius from the agent.- Hide quoted text - - Show quoted text - Why are we constraining outselves to the rabbit moving in a spiral or > along the radius of a circle? Could there not be a solution where the > rabbit moves in an elliptical path, allowing the agent to gain and > lose ground relative to the rabbit until the rabbit finds itself > opposite the agent, but closer to the edge than a circular path would > bring it? When the rabbit is further from the center than a circular path would take it, its angular velocity is necessarily less than that of the agent, so the agent is decreasing the angle, and therefore the rabbit cannot catch up to the opposite side of the diameter through the agent. Dave === Subject: Re: Diagonal wanderings (incongruent by construction) Face facts: Cantor's diagonal proof that |R| > |N| is SIMPLE. It has > even been CHECKED BY COMPUTERS. Formal proofs are irrelevant to the diagonal argument: they have it > embedded, as an informing principle, into their axioms and > definitions. Why should we believe this assertion of yours? > You have made it several times, and not yet given the slightest > reason for anyone to believe it. There has been a discussion specifically on this in the thread Levy > proof that R is uncountable: > I have been following the thread. You have rightly said that logical priority is different from historical > priority. At no point have you or anyone else given us any reason > to suppose that the diagonal argument is embedded into the axioms > and definitions of either classical or constructive theories > of the real numbers. You can say that nobody has explicitly acknowledged it, but this point > is clear enough. I just won't go back collecting links on this too, I > can't take the burden of what is rather a problem of generalised > denial. There is denial at work, indeed. > -LV -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) There is denial at work, indeed. No there isn't. note, I didn't say who was in denial; I thought that was fairly obvious .... > Brian Chandler -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) There is denial at work, indeed. No there isn't. note, I didn't say who was in denial; > I thought that was fairly obvious .... Ah, sorry! I've just realised your statement above is simply undeniable. Brian Chandler === Subject: Re: Diagonal wanderings (incongruent by construction) Let's look at total functions taking two natural numbers and returning > either 0 or 1, eg f(n,m). If we leave out the question of > multiple representations, let's suppose you have implemented > such a total function. Great. So, the anti-diagonal is itself something given algorithmically, > and you can easily write the procedure to return its nth digit, > provided that the given listing of reals itself is a total > function -- this does not mean that all the digits involved must > be computed, of course! My point (my take) is that this simply does not solve our issue: the > fact that the anti-diagonal does not belong to the list cannot be > proven from the algorithmic definition alone. The key issue is what > happens at infinity, and my thesis, to report it here in short, is > that the anti-diagonal, as any other computable string, is simply > there, in the range of a putative function 'f' like you describe > above: there is no member missing. All that is claimed by the diagonal argument in this context is > that for every *natural number* n, the anti-diagonal > differs from sequence f(n,0), f(n,1), f(n,2), ... > And that we can show fairly easily -- it looks from your post > here that you accept that. So the conclusion is that the anti-diagonal does not appear > as a row in the *given* listing -- nothing more than that. The conclusion is still unwarranted: the fact that the anti-diagonal > does not belong to the list cannot be proven from the algorithmic > definition alone. If you refuse all notion of proof *about* algorithms, then you are right that no-one can show anything about any algorithm. Is that what you want to say? If not, what sort of reasoning about algorithms is acceptable to you? > -LV -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > All that is claimed by the diagonal argument in this context is > that for every *natural number* n, the anti-diagonal > differs from sequence f(n,0), f(n,1), f(n,2), ... > And that we can show fairly easily -- it looks from your post > here that you accept that. So the conclusion is that the anti-diagonal does not appear > as a row in the *given* listing -- nothing more than that. The conclusion is still unwarranted: the fact that the anti-diagonal > does not belong to the list cannot be proven from the algorithmic > definition alone. If you refuse all notion of proof *about* algorithms, then > you are right that no-one can show anything about any algorithm. I have said the *conclusion* cannot be proven *from* the algorithmic definition alone. I am not refusing any algorithmic notions, quite the opposite! (Denial at work?) -LV === Subject: Re: Diagonal wanderings (incongruent by construction) All that is claimed by the diagonal argument in this context is > that for every *natural number* n, the anti-diagonal > differs from sequence f(n,0), f(n,1), f(n,2), ... > And that we can show fairly easily -- it looks from your post > here that you accept that. So the conclusion is that the anti-diagonal does not appear > as a row in the *given* listing -- nothing more than that. The conclusion is still unwarranted: the fact that the anti-diagonal > does not belong to the list cannot be proven from the algorithmic > definition alone. If you refuse all notion of proof *about* algorithms, then > you are right that no-one can show anything about any algorithm. I have said the *conclusion* cannot be proven *from* the algorithmic > definition alone. I am not refusing any algorithmic notions, quite the > opposite! (Denial at work?) I didn't say you were refusing algorithmic notions; what you have not said is what counts as acceptable proof *about* properties of algorithms. And you are right that if you refuse logic, and simply write programs, then there is nothing to be said about properties that the algorithms might or might not have. You haven't denied or accepted that this is your position, I note, and it's one way to take your comment from the algorithmic definition alone. In the case at hand there is a simple proof in constructive logic that the algorithm has the property that, given any effective enumeration of effective reals in the sense we are using, we have defined an effective computation of a digit sequence whioh is not at any index of the original list. So, since you deny the *possibility* of any such proof, it becomes important to establish what sort of arguments you would find acceptable to establish claims *about* algorithms, if any. > -LV -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > In the case at hand there is a simple proof in constructive logic that the > algorithm has the property that, given any effective enumeration of > effective reals in the sense we are using, we have defined an effective > computation of a digit sequence whioh is not at any index of the > original list. You keep misinterpreting on this: as said, I have no particular objections to defining an effective computation for the anti- diagonal. That the sequence so defined is not in the list at any index is what I am questioning: that *conclusion* requires a leap to infinity that cannot be proven from the algorithmic (effective) definitions only. IOW, that's a result that is *not* entailed by the algorithmic (effective) properties of the definitions in question. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) In the case at hand there is a simple proof in constructive logic that the > algorithm has the property that, given any effective enumeration of > effective reals in the sense we are using, we have defined an effective > computation of a digit sequence whioh is not at any index of the > original list. You keep misinterpreting on this: as said, I have no particular > objections to defining an effective computation for the anti- > diagonal. That the sequence so defined is not in the list at any index > is what I am questioning: that *conclusion* requires a leap to > infinity that cannot be proven from the algorithmic (effective) > definitions only. IOW, that's a result that is *not* entailed by the > algorithmic (effective) properties of the definitions in question. You keep saying this, and I keep asking you to clarify what *you* mean when you say that something is not entailed by algorithmic properties, and you simply repeat your assertions. You simply ignore my remark that there is a proof of the result you say cannot be proved. If you refuse to say what counts as proof, then of course you make it very hard for someone to come up with an argument you might accept -- that could well be your intention, of course ... Let's try this step by step; what sort of properties of an algorithm do you think *can* be proved: let's take an algorithm that takes as input a natural number, and outputs double the input. in your view, is it *possible* to show that such an algorithm never outputs 3 ? > -LV -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) > [idiotic nonsense] > Let's try this step by step; [etc. etc.] This guy is a classic crank. Why do you imagine, as you seem to do, that there is any point arguing with him? (Torkel Franzen) Herb === Subject: Re: Diagonal wanderings (incongruent by construction) > [idiotic nonsense] > Let's try this step by step; [etc. etc.] This guy is a classic crank. Why do you imagine, as you seem to do, > that there is any point arguing with him? (Torkel Franzen) I'm not the first to point out that he can accept (some) new arguments, and (sometimes) ask reasonable questions. Not a classic, then ... > Herb -- Alan Smaill === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Can you supply a natural number n, that the program won't print? No. There are infinitely many natural numbers that will never be > printed. > It is impossible to supply one of them. Provided that an actually completed infinite set N of natural numbers exists, then we would have this antinomy, among many others. === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) WM continues to deliberately confuse elements and sets of elements. One such property is that every natural number has even or odd > cardinality. One such property is that every set of natural numbers has even or odd > cardinality. That's because sets of natural numbers consist of natural numbers and are counted by natural numbers. But as usual you snipped the essential point: One such property is that every set of natural numbers has even or odd cardinality. If you know this, you can exclude that there is a set of natural numbers with cardinal number aleph_0 (because aleph_0 + 1 = aleph_0). Yes, such conjectures could be done, if infinity would follow the same logic as finity. But it seems it doesn't. So why do you believe it does in case of Cantor's simple idea? === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > WM continues to deliberately confuse elements and sets of elements. One such property is that every natural number has even or odd > cardinality. > Look! Over There! A Pink Elephant! One such property is that every set of natural numbers has even or odd > cardinality. That's because sets of natural numbers consist of natural numbers of course > and are counted by natural numbers. Piffle. No set of natural numbers without a last element is counted by a natural number. - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) WM continues to deliberately confuse elements and sets of elements. One such property is that every natural number has even or odd > cardinality. > Look! Over There! A Pink Elephant! One such property is that every set of natural numbers has even or odd > cardinality. That's because sets of natural numbers consist of natural numbers of course and are counted by natural numbers. Piffle. No set of natural numbers without > a last element is counted by a natural number. There is no natural number called out a last element. There is no set of natural numbers that cannot be counted by natural numbers. All natural numbers count themselves. === Subject: Re: Diagonal wanderings (incongruent by construction) > WM continues to deliberately confuse elements and sets of elements. > One such property is that every natural number has even or odd > cardinality. > Look! Over There! A Pink Elephant! > One such property is that every set of natural numbers has even or > odd cardinality. > That's because sets of natural numbers consist of natural numbers > of course > and are counted by natural numbers. > Piffle. No set of natural numbers without > a last element is counted by a natural number. There is no natural number called out a last element. > There is no set of natural numbers that cannot be counted by natural > numbers. > All natural numbers count themselves. > ROTFL -- W. Hughes, in sci.math.: No set of natural numbers without a last element [is finite] Prof. Dr. W. M.9fckenheim, mathematical mastermind of Augsburg University of Applied Science: There is no natural number called out a last element. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > You can't do the same for the reals. That's because the reals > aren't countable and the naturals are. That ultimately depends on your stance on the diagonal argument. No. The reals _are_ uncountable. This has nothing to do with > one's stance on the diagonal argument - the argument is > correct, regardless of anyone's stance on it. Apart from the apparent dogmatism, what you state is incorrect and, > strictly speaking, false. So it is. the formalist concludes: aleph-one is greater than aleph-null, a proposition, that has no meaning for the intuitionist. (Brouwer) === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > So what? Yes, there is no problem whatever down a list of reals, > in fact rationals, such that every real number is a _limit point_ > of the sequence. That's not news, that's not controversial, that's > awesomely well known. Nevertheless there has _never_ been a limit point of a sequence or series with irrational limit that has been defined or identified by a sequence of digits. A _limit point_ of the range of f is not the same thing as an > _element of_ the range of f. The assertion is that there is > a real number that is not _in_ the range of f. And this real number is defined by a function and not by a sequence of digits. In case you don't see the difference, let's talk about a related > situation there are many firm definitions of pi, but nobody will ever be able to give a decimal expansion that is unique for pi. Why does Cantor's argument work with the torsi of the alleged numbers and not with those definitions which define the numbers exactly? === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) >That ultimately depends on your stance on the diagonal argument. No. The reals _are_ uncountable. If there are reals that form an uncountable set, then these numbers cannot be accessed in any way, neither by diagonal arguments nor other methods. Therefore those reals that are accessible by any means that defines a number, including the diagonal argument *if it defines a number*, belong to a countable set. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=XCUCvgoAAABlmCNe8zxrKKtQU5PKSV4J Gecko/2008121300 SUSE/3.0.5-1.1 Firefox/3.0.5,gzip(gfe),gzip(gfe) That ultimately depends on your stance on the diagonal argument. No. The reals are uncountable. If there are reals that form an uncountable set, then these numbers > cannot be accessed in any way, neither by diagonal arguments nor other > methods. Therefore those reals that are accessible by any means that > defines a number, including the diagonal argument *if it defines a > number*, belong to a countable set. > Aehh, are you thinking of an uncountable set as equivalent to a physical drawer cabinet with infinite small drawers. And that gives you a problem because you can't find a pair of tweezers small enough to handle the drawers - ok, that was a stupid suggestion, but your statement seems based on some physically constrain. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Fields medal. It's not unreasonable to guess that many > mathematicians around the world would do research that > would earn them a Fields medal, the most prestigious prize > in all of mathematics. So if, as MoeBlee might be implying here, very _few_ > mathematicians seek a proof of ~Con(ZFC), then they likely > believe that no proof is possible. And if this is really > the case, then this would actually _prove_ the point that > I was making to _Mariano_ -- that the more time passes, > the less likely a proof of ~Con(ZFC) will be found, and > the fewer mathematicians will even search for a proof! The first proof that ZFC is inconsistent, to my knowledge, was the proof that there are only countably many definitions. A number that rules out any chance of access cannot belong to that uncountable set of numbers that is proven to exist by the diagonal proof (if the diagonal numbers permit access). There is no chance to define one of those undefinable numbers. So they may exist where ever they do and who ever wants to may believe in them. But they are not those numbers which appear as a diagonal of a list, because those can be defined, hence belong to a countable set. Therefore this proof is a contradiction that cannot be avoided by the hidden set of undefinable numbers. But these facts are not widely known even among set theorists. For instance, one of that illustrious society who call themselves Fools Of particular real number that is undefinable in any (countable) language? === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > That problem is easily fixed. Instead of printing out each natural > as a separate string of digits, this new program will print out > each natural as a base-1 number, i.e., as a string of '1' digits: 10 LET I = 0 > 20 PRINT I; > 30 GOTO 10 Now each and every natural will be printed. But for each number that you have printed there exist infinitely many numbers (somehow, somewhere) that remain unprinted. How can that be unless every and smaller =/= all which is a false theorem? === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > You can write a program to output all of the naturals. This program > won't halt, as you say, and for any natural n, will eventually output > n. (We are glossing over some resource limits here, but that is > customary and reasonable.) It will never finish running, though; > there are always more naturals. You can't do the same for the reals. That's because the reals > aren't countable and the naturals are. That ultimately depends on your stance on the diagonal argument. My stance controls what programs it is possible to write, you say? > So if I change my stance, a different set of things become > computable? I Did Not Know That. Most do not know that. Nevertheless it is true (if actual infinity can be finished, i.e., under generally accepted conditions). Use all binary sequences that end by zeros only, and construct the complete infinite binary tree, i.e., all its nodes and edges. Then there is nothing remaining, in the binary tree, that could be used to construct the sequence 0.010101... = 1/3. (Nevertheless all its nodes are there.) But if you use all binary sequences that end by the period 010101..., then you can construct the same tree, i.e., all its nodes and edges, and then 1/3 is in the tree. (The solution of this paradox is of course that there is nothing like the complete binary tree with all its nodes and edges, i.e., the generally accepted conditions are false.) === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=ur107QkAAAAh8RGzP83dbOXW0aXSoPPQ Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > [...] Face facts: Cantor's diagonal proof that |R| > |N| is SIMPLE. It has > even been CHECKED BY COMPUTERS. Therefore the only way that |R| = |N| > is if the various formulations of axiomatic set theory are internally > INCONSISTENT (which is emphatically NOT the same as being inconsistent > with someone's naive intuitions). Proving (say) ZFC to be inconsistent > would be worth at least a Fields Medal and a centrefold picture in the > difficult) to do then it would already have been done. The chance of > you doing it is vanishingly small. Plus, there are good reasons for believing that ZFC etc. ARE internally > consistent. For example, there is an intuitively not-unreasonable model > for ZFC etc. (Goedel's constructible universe). So your intuition tells you that ZFC is consistent. Mine tells me otherwise. Here is a simple argument for the inconsistency of ZFC. If Cantor's diagonal argument is correct, there are uncountably many real numbers in each interval of the form [-1/2n, 1/2n], where n (=1,2,3....) is a positive integer. The intersection of all such intervals (over all the positive integers n) however, contains the single real number 0. Our intuition tells us that the intersection should also contain uncountably many reals, i.e., the intersection should be an interval. Each (or every) one of the nested intervals has end-points fixed away from zero, so how come their intersection manages to eliminate all points other than zero, which does not seem possible on any reasonable conception of each (or every or all)? Now let us bring in non-standard analysis, e.g. Nelson's Internal Set Theory (IST). It is proven that IST is consistent if and only if classical ZFC is consistent, so an inconsistency in IST amounts to an inconsistency in ZFC. In IST, consider the intersection I-rho of all real intervals of the form [-1/2n, 1/2n], where n is a positive integer ranging over 11, rho>2, ... and [rho > every standard finite positive integer]. Note that IST does not consider the set of all intervals of the form [-1/2n,1/2n], where n is a standard finite positive integer, as legitimate. So the intersection of all such intervals is not legitimate either. If it were, IST would be forced to accept that the intersection consists of the single point zero, but this would be a contradiction in IST of its Principle of Internalisation (i.e., the I in IST). Conclusions: 1. If we accept that rho is an infinite integer, we would obtain a contradiction with the classical ZFC result that the intersection I- rho must consist of a single point 0; such a contradiction is avoided only by the dubious strategy of labeling rho as an internally finite integer, *despite* the fact that it exceeds every standard finite positive integer. If we refuse to relabel infinite entities as internally finite, we have to conclude IST is inconsistent, and hence, so is ZFC. 2. Secondly, IST would run into internal contradictions if it permitted a direct formulation of the intersection in terms of all (and only) intervals of the form [-1/2n,1/2n], where n is a standard positive integer. So it has to avoid contradiction by denying that such a set of intervals exists, even though classical real analysis permits precisely the same set.Thus we see that a classical ZFC result *would* be a contradiction in IST, and such a contradiction is avoided only by the tactic of making the result impossible to formulate in IST. But no convincing logical reason is provided as to why this entity is illegitimate, other than by dictat. 3. The above formulation of the paradox is precisely what Zeno found 2300 years ago. Another way of stating Zeno's paradox is to ask how infinitely many intervals [-1/2n, 1/2n] of finite non-zero length can sum to a finite length. Again IST avoids contradiction either by the dubious tactic of labelling an infinite entity as internally finite, or by denying that the set of standard intervals in question exists. In the logic NAFL (e.g. see < http://arxiv.org/abs/math/0506475 >) relabeling infinite entities as finite is not allowed and there are no such things as nonstandard finite sets. Edward Nelson says, (after noting the strange IST theorem that there must exist a finite set containing all standard finite sets), that maybe finite does not mean what we always thought it meant. Sorry, Ed, old boy, finite means what we always thought it meant, and what we always *defined* it to mean. It is IST that is inconsistent, and hence, so is ZFC. Secondly, NAFL also rejects the existence of the set of intervals mentioned in 2. above, but with the valid logical reason that infinite sets do not exist; all infinite classes are proper classes and quantification over proper classes is not permitted, and an arbitrary proper class (e.g. an arbitrary real number) does not exist. In NAFL, Cantor's diagonal argument cannot be formulated because it involves quantification over reals. This is similar to what IST does in 2. above to avoid contradiction, except that a valid logical reason is provided for why the entity in question is illegitimate. A revised version of the following paper of mine is now under review by a mainstream physics journal for the past six months: http://arxiv.org/abs/quant-ph/0504115 I am hoping that this paper will be accepted. The original submission was made in April 2005 and the revised version in Nov 2008 following a referee report in 2006 May. This paper shows why NAFL is a suitable logic in which to frame quantum mechanics, and refutes Afshar's argument that Bohr's complementarity principle has been falsified by his published experiment. === Subject: Re: Diagonal wanderings (incongruent by construction) said: > [...] > Face facts: Cantor's diagonal proof that |R| > |N| is SIMPLE. It has > even been CHECKED BY COMPUTERS. Therefore the only way that |R| = > |N| is if the various formulations of axiomatic set theory are > internally INCONSISTENT (which is emphatically NOT the same as being > inconsistent with someone's naive intuitions). Proving (say) ZFC to > be inconsistent would be worth at least a Fields Medal and a > even less than extremely difficult) to do then it would already have > been done. The chance of you doing it is vanishingly small. > Plus, there are good reasons for believing that ZFC etc. ARE > internally consistent. For example, there is an intuitively > not-unreasonable model for ZFC etc. (Goedel's constructible > universe). > So your intuition tells you that ZFC is consistent. Mine tells me > otherwise. Here is a simple argument for the inconsistency of ZFC. If Cantor's > diagonal argument is correct, there are uncountably many real numbers > in each interval of the form [-1/2n, 1/2n], where n (=1,2,3....) is a > positive integer. The intersection of all such intervals (over all the > positive integers n) however, contains the single real number 0. Our > intuition tells us that the intersection should also contain > uncountably many reals, i.e., the intersection should be an interval. Unlike many alleged intuitions that differ from my own on one matter or another, I cannot even get an inkling of yours. The intersection of a set S of sets is simply the set of things common to every set in S. Is it not obvious and intuitive to you that, for any nonzero real r in [-1/2, 1/2], there is an n such that r is not in [-1/2n, 1/2n], i.e., that there is an interval of the sort in question whose endpoints are closer to 0 than r? And hence that 0 is the only element common to the intervals in question? > Each (or every) one of the nested intervals has end-points fixed away > from zero, so how come their intersection manages to eliminate all > points other than zero,...? Well, as just noted. The fixed endpoints get closer and closer to 0 and hence, for any given nonzero real r, they eventually get closer to 0 than r. > ...which does not seem possible on any reasonable conception of each > (or every or all) Quite the contrary. One thing I find puzzling is that I don't see where the uncountability of the intervals in question makes any difference to your reasoning. If we were to replace those intervals in your argument with the sets of rationals in those intervals, it seems to me that your intuition should likewise tell you that there should be countably many rationals in their intersection. What (if anything) is the difference in the two cases? Is your idea that we shouldn't be able to eliminate uncountably many reals by means of a countable process (i.e., one where we move from [-1/2n, 1/2n] to [-1/2(n+1), 1/2(n+1)])? But this would be a problem only if each step in the process only eliminated countably many reals. I just don't see where you are coming from at all. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > Here is a simple argument for the inconsistency of ZFC. If Cantor's > diagonal argument is correct, there are uncountably many real numbers > in each interval of the form [-1/2n, 1/2n], where n (=1,2,3....) is a > positive integer. The intersection of all such intervals (over all the > positive integers n) however, contains the single real number 0. Our > intuition tells us that the intersection should also contain > uncountably many reals, i.e., the intersection should be an interval. > Each (or every) one of the nested intervals has end-points fixed away > from zero, so how come their intersection manages to eliminate all > points other than zero, which does not seem possible on any reasonable > conception of each (or every or all)? I hope I'm not taking anything out of context, but I'd just like to look at this first paragraph. I assume that this alone is supposed to be at least a preliminary justification of your apparent intuition. Consider set rake(n) n a natural number, defined as: { x = a/bn | a, b are naturals, and -1 < x < 1 } (In other words, rake(p) is the set of rationals in (-1, 1) with a p in the denominator.) Each rake includes an infinite number of elements. For any two, rake (m) and rake(n), the intersection includes all rationals in the range with m*n in the denominator. Another infinite set. For any finite set of rakes, the intersection is another rake: Intersect (rake_j1, ...rake_jn) = rake(lcm(rake_j1...rake_jn) Yet the intersection of _all_ the rakes consists only of 0. Do you consider this too to be counterintuitive. (I don't, but if you don't either, you need to explain the difference from the case above.) In particular, I cannot understand the significance of this bit: > ... does not seem possible on any reasonable > conception of each (or every or all)? What sort of conception of each, every and all do you have? Brian Chandler === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=ur107QkAAAAh8RGzP83dbOXW0aXSoPPQ Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > [...] Face facts: Cantor's diagonal proof that |R| > |N| is SIMPLE. It has > even been CHECKED BY COMPUTERS. Therefore the only way that |R| = |N| > is if the various formulations of axiomatic set theory are internally > INCONSISTENT (which is emphatically NOT the same as being inconsistent > with someone's naive intuitions). Proving (say) ZFC to be inconsistent > would be worth at least a Fields Medal and a centrefold picture in the > difficult) to do then it would already have been done. The chance of > you doing it is vanishingly small. Plus, there are good reasons for believing that ZFC etc. ARE internally > consistent. For example, there is an intuitively not-unreasonable model > for ZFC etc. (Goedel's constructible universe). So your intuition tells you that ZFC is consistent. Mine tells me > otherwise. Here is a simple argument for the inconsistency of ZFC. If Cantor's > diagonal argument is correct, there are uncountably many real numbers > in each interval of the form [-1/2n, 1/2n], where n (=1,2,3....) is a > positive integer. The intersection of all such intervals (over all the > positive integers n) however, contains the single real number 0. Our > intuition tells us that the intersection should also contain > uncountably many reals, i.e., the intersection should be an interval. > Each (or every) one of the nested intervals has end-points fixed away > from zero, so how come their intersection manages to eliminate all > points other than zero, which does not seem possible on any reasonable > conception of each (or every or all)? Now let us bring in non-standard analysis, e.g. Nelson's Internal Set > Theory (IST). It is proven that IST is consistent if and only if > classical ZFC is consistent, so an inconsistency in IST amounts to an > inconsistency in ZFC. In IST, consider the intersection I-rho of all > real intervals of the form [-1/2n, 1/2n], where n is a positive > integer ranging over 1 integer. The intersection I-rho *is* an interval (containing > uncountably many points) around 0 after all, *despite* the fact rho > satisfies rho>1, rho>2, ... and [rho > every standard finite positive > integer]. Note that IST does not consider the set of all intervals of the form > [-1/2n,1/2n], where n is a standard finite positive integer, as > legitimate. So the intersection of all such intervals is not > legitimate either. If it were, IST would be forced to accept that the > intersection consists of the single point zero, but this would be a > contradiction in IST of its Principle of Internalisation (i.e., the > I in IST). > Sorry I meant the Idealization principle (not Internalization as I had stated above). IST also stands for the three principles of Internal Set Theory, namely Idealization, Standardization and the Transfer Principle. > Conclusions: 1. If we accept that rho is an infinite integer, we would obtain a > contradiction with the classical ZFC result that the intersection I- > rho must consist of a single point 0; such a contradiction is avoided > only by the dubious strategy of labeling rho as an internally finite > integer, *despite* the fact that it exceeds every standard finite > positive integer. If we refuse to relabel infinite entities as > internally finite, we have to conclude IST is inconsistent, and > hence, so is ZFC. 2. Secondly, IST would run into internal contradictions if it > permitted a direct formulation of the intersection in terms of all > (and only) intervals of the form [-1/2n,1/2n], where n is a standard > positive integer. So it has to avoid contradiction by denying that > such a set of intervals exists, even though classical real analysis > permits precisely the same set.Thus we see that a classical ZFC result > *would* be a contradiction in IST, and such a contradiction is avoided > only by the tactic of making the result impossible to formulate in > IST. But no convincing logical reason is provided as to why this > entity is illegitimate, other than by dictat. > In fact the Idealization principle captures precisely the intuition that tells us that an intersection of infinitely many intervals of the form [-1/2n,1/2n] must include an interval. 3. The above formulation of the paradox is precisely what Zeno found > 2300 years ago. Another way of stating Zeno's paradox is to ask how > infinitely many intervals [-1/2n, 1/2n] of finite non-zero length can > sum to a finite length. Again IST avoids contradiction either by the > dubious tactic of labelling an infinite entity as internally finite, > or by denying that the set of standard intervals in question exists. In the logic NAFL (e.g. see ) > relabeling infinite entities as finite is not allowed and there are no > such things as nonstandard finite sets. Edward Nelson says, (after > noting the strange IST theorem that there must exist a finite set > containing all standard finite sets), that maybe finite does not mean > what we always thought it meant. Sorry, Ed, old boy, finite means > what we always thought it meant, and what we always *defined* it to > mean. It is IST that is inconsistent, and hence, so is ZFC. > Indeed, if we did not accept that finite means what we always thought it meant, we wouldn't even know what a theory is. The basic principles of logic are dependent on our knowing the meaning of the word finite and that meaning cannot be tampered with. Secondly, NAFL also rejects the existence of the set of intervals > mentioned in 2. above, but with the valid logical reason that > infinite sets do not exist; all infinite classes are proper classes > and quantification over proper classes is not permitted, and an > arbitrary proper class (e.g. an arbitrary real number) does not > exist. In NAFL, Cantor's diagonal argument cannot be formulated > because it involves quantification over reals. This is similar to what > IST does in 2. above to avoid contradiction, except that a valid > logical reason is provided for why the entity in question is > illegitimate. A revised version of the following paper of mine is now under review > by a mainstream physics journal for the past six months: http://arxiv.org/abs/quant-ph/0504115 I am hoping that this paper will be accepted. The original submission > was made in April 2005 and the revised version in Nov 2008 following a > referee report in 2006 May. This paper shows why NAFL is a suitable > logic in which to frame quantum mechanics, and refutes Afshar's > argument that Bohr's complementarity principle has been falsified by > his published experiment. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > I'm surprised no one mentioned that this program will eventually either > crash with an overflow (if I is of an integer type) or stop counting (if > I is of a floating-point type, where once it hits a certain size it will > discard the least-significant bits). Of course, your variable could be > all the natural numbers have been counted (and I'd like to see someone > implement bigint in basica That is in fact an important argument and it prevents us from the traps of infinity. The universe has about 10^80 atoms and never will have more. Therefore it is impossible to include any natural number in the counting-sequence that requires more than 10^80 bits for its identification. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=UJeUTgkAAADYai-ULU41ORCvNnkXmdRu Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) | | > impredicative, so constructively invalid. No, this is a confusion on the concept of predicativity. The proof is predicative. | It is not at all clear that constructivism in itself requires absence | of impredicativity. Though, of course, certain currents in constructivism do |absence of predicativity. I think using constructive to mean predicative as well is liable to lead to some confusion, usually, so I would avoid it. Two properties that seem very natural to require are the number existence and set existence principles. The numeric existence principle for an axiom system says that there's a procedure for taking a proof that there exists an integer having some given property, and from it extracting a specific example of such an integer. The set existence principle likewise says that from a proof of the existence of a set one can extract an example of the form {x : P(x)} for a given formula P. The numeric existence principle is the more important one. It implies under usual conditions a principle called the disjunction principle, namely, that if P or Q is provable, then either P is provable or Q is provable. (Usually one can prove P or Q if and only if one can prove the existence of an integer n such that if n=0 then P and if n<>0 then Q, and exhibiting such an n allows us to prove P or prove Q.) I would say that a system satisfying these properties can legitimately be called constructive. A constructivist won't necessarily consider it a suitable system for developing mathematics in, but the same goes for everybody else. People (e.g. Maddy) have made stabs at giving criteria for what counts as a good system, but it never as far as I know boils down to something as simple as being constructive. One advantage of showing this tiny bit of leniency is that logicians have found for most formal systems on the ladder of strengths of system, a counterpart which is almost the same except for using intuitionistic logic. It seems appropriate to me to just think of these as the constructive counterparts of the classical systems. | Anyway, the point stands that while a constructivist might not accept | certain axioms, the LOGIC in the proof is intuitionistic. The logic is intuitionistic, yes, and the proof is predicative too. Impredicativity does not arise just from constructing a real from a set having reals as members (or members of members, etc.). The new real is not a member of any of the sets previously mentioned in the proof (or a member of a member, etc.) In Weyl's The Continuum , he has a predicative system, and in it the existence of a least upper bound of a sequence of reals bounded above is provable, but not the existence of a least upper bound of an arbitrary set of reals. | Moreover, certain constructivists DO explicitly endorse that the proof | IS constructive. Yes, because there's nothing wrong with it. There's the technical problem with one proof, in that it's not constructive that each real has a decimal expansion. But the proof as given works for reals having decimal expansions, plus Cantor's earlier proof of the same result doesn't have the technical difficulty, as it doesn't rely upon decimal expansions. If you take a system like in Principia Mathematica without the reducibility axiom, I believe you might have to say that the new real is on another level of the hierarchy from the ones from which it is constructed. By the same token, there's no set of all reals in that system. I don't think that deserves to be thought of as a problem. |But, of course, that may be while we note that the | interpertation of the theorem in constructivism is different from in | classical mathematics. Not too severely different. The main difference is that as constructively interpreted the result is a little stronger; it tells you that you can actually exhibit the new real number. Keith Ramsay === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Not too severely different. The main difference is that as > constructively interpreted the result is a little stronger; > it tells you that you can actually exhibit the new real > number. And that is false because no irrational number can be uniquely defined by parts of its decimal expansion - and the complete expansion, complete enough to distinguish the diagonal from every other number (not only from every _given_ number (that's a difference, because not all numbers can be given)), is inaccessible. But that is not the concern of every constructivist. Brouwer for instance said: According to the statements previously made, this power aleph-null is the only infinite power of which the intuitionists recognize the existence. Let us now consider the concept: denumerably infinite ordinal the fact that this concept has a clear and well-defined meaning for both formalist and intuitionist, the former infers the right to create the set of all denumerably infinite ordinal numbers, the power of which he calls aleph-one, a right not recognized by the intuitionist. Because it is possible to argue to the satisfaction of both formalist and intuitionist, first, that denumerably infinite sets of denumerably infinite ordinal numbers can be built up in various ways, and second, that for every such set it is possible to assign a denumerably infinite ordinal number, not belonging to this set, the formalist concludes: aleph-one is greater than aleph- null, a proposition, that has no meaning for the intuitionist. Because it is possible to prove to the satisfaction of both formalist and intuitionist, first, that denumerably infinite sets of real numbers between 0 and 1 can be constructed in various ways, and second that for every such set it is possible to assign a real number between 0 and 1, not belonging to the set, the formalist concludes: the power of the continuum, i. e., the power of the set of real numbers between 0 and 1, is greater than aleph-null, a proposition which is without meaning for the intuitionist; the formalist further raises the question, whether there exist sets of real numbers between 0 and 1, whose power is less than that of the continuum, but greater than aleph-null, in other words, whether the power of the continuum is the second smallest infinite power, and this question, which is still waiting for an answer, he considers to be one of the most dificult and most fundamental of mathematical problems. For the intuitionist, however, the question as stated is without meaning; and as soon as it has been so interpreted as to get a meaning, it can easily be answered. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > | > | > impredicative, so constructively invalid. No, this is a confusion on the concept of predicativity. The > proof is predicative. I might very well be missing something, but I read on Wikipedia: http://en.wikipedia.org/wiki/Impredicativity --- In mathematics and logic, impredicativity is the property of a self-referencing definition. More precisely, a definition is said to be impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set which contains the thing being defined. I note here that self-referential mention seems enough, no need for quantification over. --- Russell's paradox is a famous example of an impredicative construction, namely the set of all sets which do not contain themselves. --- Concerning mathematics, an example of an impredicative definition is the smallest number in a set, which is formally defined as: y = min(X) if and only if for all elements x of X, y is less than or equal to x, and y is in X. --- The greatest lower bound of a set X, glb(X), generalizes this concept; y = glb(X) if and only if for all elements x of X, y is less than or equal to x, and any z less than or equal to all elements of X is less than or equal to y. But this definition also quantifies over the set (potentially infinite, depending on the order in question) whose members are the lower bounds of X, one of which being the glb itself. Hence predicativism would reject this definition. I'll take also the chance to note that, while I keep disagree that Cantor's arguments (any of them) are perfectly constructive, as has been claimed, my objection to the diagonal argument here does not leverage predicativity at all: I have tried to focuses on what to me seems an unwarranted conclusion. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) (I hope I've stated that fairly accurately. But you can also check a > textbook in mathematical logic under the subject of interpreting one > theory in another, however it is actually worded in the book.) -- hz === Subject: Re: Diagonal wanderings (incongruent by construction) Can you supply a natural number n, that the program won't print? No. Wolenmuekenheim logic There are infinitely many natural numbers that will never be > printed. > It is impossible to supply one of them. Yeah, Bill, it's absurd. Why do you continue to respond to this loon? Do you think that one day you'll back him into a corner and he'll say, Yeah, you're right, I'm mistaken? Why won't you just let this spavined donkey die a natural death? -- hz === Subject: Re: Diagonal wanderings (incongruent by construction) > Can you supply a natural number n, that the program won't print? > No. Wolenmuekenheim logic There are infinitely many natural numbers that will never be > printed. > It is impossible to supply one of them. > Yeah, Bill, it's absurd. Why do you continue to respond to this loon? Do you think that > one day you'll back him into a corner and he'll say, Yeah, you're > right, I'm mistaken? Why won't you just let this spavined donkey die a natural death? I'd like to vote for an unnatural death, if I may? Phil -- Marijuana is indeed a dangerous drug. It causes governments to wage war against their own people. -- Dave Seaman (sci.math, 19 Mar 2009) === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > On May 8, 10:36am, Mariano Su.87rez-Alvarez And their programmers want them to formulate proofs in the > dominant theory, not in alternate theories. > Programmers are mostly theory-agnostic when they are > programming provers. What on earth suggests to you > that, say, Prover9 is restricted to (whatever it is > that you consider) dominant set theory? By dominant set theory I usually mean ZFC, i.e. the set > theory that most set theorists use. Well, I suppose that Prover9 isn't limited to ZFC, since > Marshall says that he was able to use it to prove theorems > in a theory whose lone axiom is Ax (Ay (x=y)), which is > hardly equivalent to ZFC. But what I've never seen is a theory that is proposed by a > so-called crank entered into Prover9, despite my attempts > to make the crank theories rigorous. Indeed, what I would > love to see is a rigorous version of a crank theory > entered into Prover9 -- and I'll consider my attempts to > make crank theories to be successful if my version of the > theory can be entered into Prover9 to prove theorems, > especially if those theorems are negations of those that > are provable in ZFC (assuming both ZFC and my proposed > theory to be consistent). That you seem to think there is such a restriction There is a restriction -- Prover9 can only give proofs > in theories that someone types into the prover. If no > one enters a rigorous version of a crank theory, then > Prover9 won't prove anything in that theory. So, you are saying that the restriction is that no one cares enough for those theories? Modulo the standard disclaimers, that is a clear indication that those theories are not interesting. That is not a restriction but a fact. > is a clear sign that you have absolutely no idea what > an automatic prover is. I'd like to know more about how Prover9 works. I've tried > asking Prover9 users how it works, but answers have not > been forthcoming. If I don't know how something works, I'd much rather be > told how it does work, not simply you don't know how > (whatever) works. But standard theorists on sci.math are > far more likely to say the latter than the former. Have you tried googling for Prover9, picking the corresponding page and then clicked on the link clearly labeled Manual and examples that is on the page? That is a strategy that most reasonable persons would have put into practice in order to know how Prover9 works. Declaiming your prejudice as to what your putative standard theoriest would or would not do is a rather inducive strategy to find out what Prover9---or anything else, for that matter---works. > The more time passes, the more likely we'll see a proof of, > say, the Riemann Hypothesis or Goldbach's Conjecture. > The more time passes, the less likely we'll see a proof that > ZFC is inconsistent. > What possible basis do you have for the two claims you make? Mathematicians all over the world are searching for proofs > of Riemann and Goldbach. As more and more time passes, it > becomes more and more likely that someone will discover a > proof of one of these conjectures. It's more likely that a > proof of RH will be discovered by 2020 than by 2010, and > it's still more likely that a proof of RH will be found by > 2100 than by 2020. Therefore, the more time passes, the > more likely that we'll see a proof of Riemann or Goldbach. Mathematicians all over the world are also searching for > proofs that ZFC is inconsistent. But, as Knox points out, > if there really is a proof of ~Con(ZFC), we most likely > would have found it by now. For many inconsistent theories > it's easy to find a proof of its inconsistency. It took > only a few years to find a contradiction in Cantor's naive > set theory, and those cranks who propose theories on > sci.math, that turn out to be inconsistent, it often takes > mere hours to find the inconsistency. But ZFC has > withstood the test of time. It seems hard to believe that > mathematicians would have overlooked an inconsistency for > so long -- well over a century. Since we haven't found a > contradiction by now, it's unlikely that we'll see one by > 2010 or 2020. And if we haven't found one by 2100, we may > as well consider ZFC to be consistent -- since we'll > likely never find a proof of ~Con(ZFC). This seems to be Since Mariano asked me, I ask the same of Mariano, and I > wonder what his opinion of the likelihood that we'll ever > see a proof of Riemann, Goldbach, or ~Con(ZFC). I have no opinion as to whether Riemann's hypothesis is any more approachable today than it was a century ago, nor on the likelyhood of its being decided one way or another in the near---or far---future. The same is true regarding Golbach's conjecture and the consistency of ZFC. > If there were a > rigorous theory in which more of their intutions are provable > than in ZFC, then maybe LV and the other opponents of the > dominant set theory would have less reason to start these > threads and complain about set theory all the time. > Can you please point to *someone* who *does* see > a reason why opponents of ZFC can't have an alternate > theory? Here are some reasons given for why opponents of ZFC can't > have an alternate theory: The alternate theories (i.e., the particular alternate > theory proposed by the particular opponent of ZFC) aren't > rigorous enough. > The alternate theories aren't coherent enough. > The alternate theories can't prove anything that is useful > to applied science. > The alternate theories are inconsistent (which even I > consider to be a valid reason). And so on. I'll leave it to Mariano to find the posters > who gave these as reasons that opponents of ZFC can't > have their alternate theories. Those are not reasons why opponents of ZFC cannot have an alternate theory. Those are reasons why the alternate theories (which, really, are not given in any form which deserves that name...) they propose are of no interest. There *is* a difference. You have shown yourself repeatedly to be immune to the distinction, though. -- m === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Continuation We have (agreed by both WM and WH) i: if all natural numbers and all lines exist then no line contains all natural numbers is true. WM claims a contradiction in that we also have ii: if all natural numbers and all lines exist then there exists a line that contains all natural numbers is true. However, if all natural numbers exist and all lines exist, then neither the set of natuaral numbers nor the set of lines has a last element. To establish the putative contradiction, we need a proof of ii that does not require a last element. WM first try: WM: Every line contains all numbers that are in the preceding lines. WM: If all numbers exist, then they exist in one line. Nope. Clearly the one line in the second statment is the last line. The second statement is not true if there is no last line. Try again. - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Continuation 1 2, 1 3, 2, 1 ... We have (agreed by both WM and WH) i: if > all natural numbers and all lines exist > then > no line contains all natural numbers is true. By the fact that for every line there is a line with one more number. WM claims a contradiction in that we also have ii: if > all natural numbers and all lines exist > then > there exists a line that contains all natural numbers is true. Because then also all lines exist. Every line contains everything that is contained in its predecessor lines. However, if all natural numbers exist and all lines exist, > then neither the set of natuaral numbers nor > the set of lines has a last element. (How then do you know that there are all?) > To establish the putative contradiction, we need a proof of ii > that does not require a last element. WM first try: WM: Every line contains all numbers that are in the preceding lines. > WM: If all numbers exist, then they exist in one line. Nope. Clearly the one line in the second statment is the last > line. > The second statement is not true if there is no last line. No. My proof uses only the linearity and the geometrical symmetry shown in the list above. The first column cannot contain more than every line. If the first column is complete, then the set of lines is as complete). The lines exist in exactly the same manner as the number of the first column. This can only be understood by non-Cantorian sets, i.e., potentiallly infinite sets. === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Continuation 1 > 2, 1 > 3, 2, 1 > ... We have (agreed by both WM and WH) i: if > all natural numbers and all lines exist > then > no line contains all natural numbers is true. > WM claims a contradiction in that we also have ii: if > all natural numbers and all lines exist > then > there exists a line that contains all natural numbers is true. > However, if all natural numbers exist and all lines exist, > then neither the set of natuaral numbers nor > the set of lines has a last element. (How then do you know that there are all?) The first part of ii reads if all natural numbers and all lines exist To establish the putative contradiction, we need a proof of ii > that does not require a last element. WM first try: WM: Every line contains all numbers that are in the preceding lines. > WM: If all numbers exist, then they exist in one line. Nope. Clearly the one line in the second statment is the last > line. > The second statement is not true if there is no last line. No. My proof uses only the linearity and the geometrical symmetry > shown in the list above. The first column cannot contain more than > every line. The first column cannot contain any *element* not contained in the lines. The first column can and does contain a *subset* not contained in the lines. Clearly the one line in the second statment is the last line. The second statement (a statement about *subsets* not *elements*) is not true if there is no last line. Try again. - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > 1 > 2, 1 > 3, 2, 1 > ... No. My proof uses only the linearity and the geometrical symmetry > shown in the list above. The first column cannot contain more than > every line. The first column cannot contain any *element* > not contained in the lines. > The first column can and does contain a *subset* > not contained in the lines. That is impossible by the fact that every element contained in the first column is also contained in one line. If a line contains all elements of S then it contains the subset S. You would like to construct a distinction between all elements of S and S. You can do so, but you must identify what distinguishes these things. Clearly the one line in the second statment > is the last line. I did not say so. But it is suggesting itself that if all elements of an ordered set exist, then there should be a last element. Because, how would you porve that all are there? > The second statement (a statement about *subsets* > not *elements*) is not true if there is no last line. You want to distinguish between all elements 1, 2, 3, ... and the the set N. Well, try to communicate a means by what this can be done. The mere assertion is not enough. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Can you supply a natural number n, that the program won't print? No. Can you understand that at *any* step there are infinitely many > numbers remaining that have not been printed and will never be > printed, because they belong to the set that is remaining after any > step? that 1 has not and never will be printed because it belongs > to the set that is remaining. That's a lame argument even for you. > I have a dream: Even matheologists should be able to understand what is easily understood by any sober mind: Every and all smaller = all for any ordered set. Of course most matheologists will be unable to understand that. But perhaps you would be willing to learn from some greater names? Û 174 Set theory is wrong (Wittgenstein) ... classical logic was abstracted from the mathematics of finite sets and their subsets .... Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. ... As Brouwer pointed out this is a fallacy, the Fall and Original sin of set theory even if no paradoxes result from it. (Hermann Weyl) Indeed, I think that there is a real need, in formalism and elsewhere, to link our understanding of mathematics with our understanding of the physical world. (Robinson) Infinite totalities do not exist in any sense of the word (i.e., either really or ideally). More precisely, any mention, or purported mention, of infinite totalities is, literally, meaningless. (Robinson) Of course, I know, all these people do not mean what they said. On the contrary, they meant exactly the opposite of what they said, because they were not cranks. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) perhaps you would be willing to learn from some greater names? Not really. I don't subscribe to the practice of fawning over ancestors. The fact that those well-respected people said such stupid things (assuming they actually did, and you've not altered the meaning by removing the context, which I will give you the benefit of the doubt on, as I have not seen dishonesty appear particularly strongly on your lengthy list of faults) is mildly surprising but not astonishing, and certainly no reason to revise modern mathematics. I am not a mathematician; I am a computer programmer. As such, I have to deal with the realities of working within systems of limited resources more than anyone doing math does. It is part of my daily, my hourly existence. I am much closer to the realities of finiteness than you. So for me, it is highly ironic that, for all your relentless fixation on finiteness, you suck at it. The best you can do is rail pointlessly against clean abstractions like the natural numbers. You complain bitterly that they don't model resource limits, but you've never been able to show a logical contradiction that results. (I know, I know; to you, failing to model resource limits is itself a contradiction. Big deal; that just shows you don't know what a contradiction is.) And of course, you haven't ever proposed any abstractions of your own that *do* model resource limits; another crank hallmark. While we're quoting greater names, I recall an essay by Dijkstra in which he discussed the importance of separation of concerns, and topically, the exact two concerns he mentioned separating were correctness and resource limits. He also touched on the frustrations of trying to deal with those people of such limited intellect as to be unable or unwilling to make the separation. Marshall PS. Everyone says stupid things now and again. And who knows? Maybe Robinson woke up the next morning with a terrible headache, and was later heard asking I said *what* last night?! === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > So for me, it is highly ironic that, for all your relentless > fixation on finiteness, you suck at it. The best you can do > is rail pointlessly against clean abstractions like the > natural numbers. You complain bitterly that they don't model > resource limits, but you've never been able to show a logical > contradiction that results. The logical contradiction has nothing to do with resource limits. The logical contradiction is: It is impossible to define any irrational number by a string of digits. But it is possible to define an irrational number by a finite definition. The number of finite definitions, however, is countable. And of course, you haven't ever proposed any abstractions > of your own that *do* model resource limits; Current mathematics (except set theory) does what is necessary. There is no reason to provide further abstractions. PS. Everyone says stupid things now and again. > And who knows? Maybe Robinson woke up the > next morning with a terrible headache, and was later > heard asking I said *what* last night?! Of course, all my quotes stem from drunk people. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=XCUCvgoAAABlmCNe8zxrKKtQU5PKSV4J Gecko/2008121300 SUSE/3.0.5-1.1 Firefox/3.0.5,gzip(gfe),gzip(gfe) So for me, it is highly ironic that, for all your relentless > fixation on finiteness, you suck at it. The best you can do > is rail pointlessly against clean abstractions like the > natural numbers. You complain bitterly that they don't model > resource limits, but you've never been able to show a logical > contradiction that results. The logical contradiction has nothing to do with resource limits. > The logical contradiction is: > It is impossible to define any irrational number by a string of > digits. > But it is possible to define an irrational number by a finite > definition. > The number of finite definitions, however, is countable. If this is an argument for the countability of the reals, then please elaborate on how these definitions are constructed. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) So for me, it is highly ironic that, for all your relentless > fixation on finiteness, you suck at it. The best you can do > is rail pointlessly against clean abstractions like the > natural numbers. You complain bitterly that they don't model > resource limits, but you've never been able to show a logical > contradiction that results. The logical contradiction has nothing to do with resource limits. > The logical contradiction is: > It is impossible to define any irrational number by a string of > digits. > But it is possible to define an irrational number by a finite > definition. > The number of finite definitions, however, is countable. Just as I said: you don't understand what a contradiction is. Hmm. We were discussing the naturals, and your resource limit based objections to the set of all of them, and then you switch to a different objection to the set of all reals. That is really quite dishonest, isn't it? I guess I will have to retract my earlier statement that I had not seen you be dishonest; I have actually seen you do this sort of switch many times. > And of course, you haven't ever proposed any abstractions > of your own that *do* model resource limits; Current mathematics (except set theory) does what is necessary. There > is no reason to provide further abstractions. If current mathematics does what is necessary, then we have no further need for new mathematics, and you have no basis to complain about anything that is being done currently. > PS. Everyone says stupid things now and again. > And who knows? Maybe Robinson woke up the > next morning with a terrible headache, and was later > heard asking I said *what* last night?! Of course, all my quotes stem from drunk people. Not necessarily; it could have been drugs. Marshall === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > So for me, it is highly ironic that, for all your relentless > fixation on finiteness, you suck at it. The best you can do > is rail pointlessly against clean abstractions like the > natural numbers. You complain bitterly that they don't model > resource limits, but you've never been able to show a logical > contradiction that results. The logical contradiction has nothing to do with resource limits. > The logical contradiction is: > It is impossible to define any irrational number by a string of > digits. > But it is possible to define an irrational number by a finite > definition. > The number of finite definitions, however, is countable. Just as I said: you don't understand what a contradiction is. The contradiction is: In mathematics based on ZFC: Every real number can be identified. Not every real number can be identified. Hmm. We were discussing the naturals, and your resource > limit based objections to the set of all of them, and I informed you that this is not my main point. My main point is the inconsistency of the actual infinite. > and then > you switch to a different objection to the set of all reals. > That is really quite dishonest, isn't it? You said: you've never been able to show a logical contradiction. So I picked just one. And of course, you haven't ever proposed any abstractions > of your own that *do* model resource limits; Current mathematics (except set theory) does what is necessary. There > is no reason to provide further abstractions. If current mathematics does what is necessary, then we have > no further need for new mathematics, and you have no basis > to complain about anything that is being done currently. Current mathematics has nothing to do with set theory. It is only set theorists who are claiming that their theory was necessarily required to provide a firm fundament for mathematics. Just the opposite is true. === Subject: Re: Diagonal wanderings (incongruent by construction) > Just as I said: you don't understand what a contradiction is. > [etc. etc.] Wolfgang M.9fckenheim is a classic crank. Why do you imagine, as you seem to do, that there is any point arguing with him? (Torkel Franzen) Herb === Subject: Prof.Dr.habil.Kutolin S.A. at all. Cybernetic models in materials posting-account=VUS2DgoAAADYN_NDly9uSUJBo5y5pr_P Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) === Subject: Re: Ordinal numbers - some doubts In message >OK then. So let me combine Hartley's and MoeBlee's comments and see how >I can apply this to Z and the proposed theory TST. We begin with Hartley's construction and let x be a wellordered >cardinal that is greater than omega. >.... I should just point out that I didn't invent that construction. I learnt it from a post of Denis Feldman's a few months ago, but I imagine something similar was used by Zermelo, maybe even Cantor. -- David Hartley === Subject: Re: Hitting a spec of debris at .97*c might kill you. posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > Would some knowledgeable person address the issue of mass energy and > maybe, just maybe suggest that neither the spec of debris nor the craft > is privileged and therefore the effect would be nil? As objects approach > c relative to each other, they each enter into the dimension of the > creation of space in which there are no privileged masses. === Subject: Re: Hitting a spec of debris at .97*c might kill you. > Would some knowledgeable person address the issue of mass energy and > maybe, just maybe suggest that neither the spec of debris nor the craft > is privileged and therefore the effect would be nil? As objects approach > c relative to each other, they each enter into the dimension of the > creation of space in which there are no privileged masses. > Why thank you, NoEinstein: considering the source, that is a compliment. === Subject: Re: Hitting a spec of debris at .97*c might kill you. posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > Folks: PD is a certifiable LUNY who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein Well, my crankometer pegs when you post NoE. NoEinstein === Subject: Re: Hitting a spec of debris at .97*c might kill you. > Folks: PD is a certifiable LUNY who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein > Well, my crankometer pegs when you post NoE. NoEinstein I do not need to use my credentials to peg you as a crack, NoE. LOL! === Subject: Re: Hitting a spec of debris at .97*c might kill you. posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > Folks: Parasites like PD should be dealt with in the most drastic ways. Unfortunately, these news groups only allow the use of words. NoEinstein Folks: PD is a certifiable LUNY You're talking about aliens walking among us, and you're calling ME a > certifiable LUNY? What's a LUNY, anyway? who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein Folks: If simple truths Like aliens walking among us? are 'incoherent babbling' to PD, then, he is > well over his head to be replying regarding such on these news > groups. NoEinstein MINUS v ) is that a warp speed spaceship can still send radar beams > ahead to locate threatening objects in time to correct the course. > Also, as I have explained, the ether near massive objects is polar. > That means such can be magnetized way out ahead of the spaceship so > that the ether will pass around the spaceship rather than pass through > it. Small objects would be caught in the ether flow like floating > sticks in a creek. If there is an obstruction, the sticks will flow > around suchwith the waterrather than impacting the obstruction. > Believe me, extraterrestrials must have worked out those > technicalities, or they wouldn't be among us today! NoEinstein the Completely-Off-My-Nut flag. It will spare me the effort of every > having to take anything you say as anything other than incoherent > babbling.- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: quartic equation I am a fan of yours and have read most of your namely (30^4+120^4+272^3+315^4=353^4 ). Susequently Simcha Brudno also gave some examples. A year ago Jacobi and Daniel Madden gave a parametric solution of above but it had a condition that ( e= a+b+c+d ) where a,b,c,d can take plus or minus values. The solution is quadratic in nature which I can send to you. I am interested actually in finding a solution without the Oliver === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > logical thinking. After enduring long books on difficult science (like... relativity), naive readers feel that they have been made to be 'learned', too. But all they now are is: brainwashed FOOLS. NoEinstein Real scientists do not do, nor report, their research on this forums. >They study the subjects, they make measurements and simulations and, >finally, report their findings in conferences and journals (that is at >least what I do). Talking of real people doing science, and working in real problems, >here are some references to read: 1) 10 General Relativistic Models for Space-time Coordinates and >XXVIIA Reports on Astronomy 2006-2009, pp55-59. >Tou Ni, Michael C.W. Sandford, Christian Veillet, An-Ming Wu, Patricia >Fridelance, Etienne >Samain, George Spalding and Xiaohui Xu, Adv. Space Res. Vol. 32, No. >4) Relativistic Corrections to Lunar Occultations, Costantino >Sigismondi, Tenth Italian-Korean Meeting on Relativistic Astrophysics >Pescara, June 25-30, 2007. >5) Deep-space laser-ranging missions ASTROD and ASTROD I for >astrodynamics and astrometry, W. T. Ni and the ASTROD I ESA COSMIC >Astrometry Proceedings IAU Symposium No. 248, 2007. Miguel Rios I was not Talking of real people doing science, > I was Talking of real people doing REALITY. As can be seen from your reference > 10 General Relativistic Models for Space-time.. > and Ashby's paper that uses 13 Classical Physics hacks > of GPS data to fit it to General Relativity, unlike DNA scientists, computer scientists, electronics scientists, etc. > all of the General Relativity Gurus seem to be guys on the Public Dole, > who have never made a real world contribution to mankind. One would think that if General Relativity Gurus > possessed such powerful, esoteric knowledge, > they would use it to make a few bucks in the free market, rather than being a burden to hardworking taxpayers, > and wasting the minds and time of young folks > on issues such as time travel, worm holes, > the beginning and end of the universe, > and the mind of God. A mind is a terrible thing to waste. -- > Tom Well Mr. potter, regarding the chicken situation, I'm quite sure you > do not need Galileo, Newton, nor Einstein theories to find your way to > your bathroom at night. That is how reality works!!. Science, on the other hand, has always worked differently to that. You > observe Nature and wonder how and why it works like like you see it. > Then you build a model that may, or may not, be useful to predict the > results of observations. Many advances on physics or mathematics take > several years to understand, and then more years to get into real > useful applications of those new advances. One example: in the early > 60's, Dr. Robert Gallager, on his Ph.D. thesis, found a mathematical > method that could be used in coding systems. The method is called Low > Density Parity Check (LDPC). For over 30 years nothing happened with > his development (even him had forgotten it), until somebody found the > method could be applied to the 3G and 4G cellular systems. So now, > almost all cellular systems are using these LDPC codes to improve the > quality of communications. Furthermore, History has shown that nobody has ever developed a new > and useful theory without being familiar with the then-current > theories and experiments. That's why the idiots and crackpots around > here are so pathetic: if they truly wanted to make a contribution, > they would be seriously STUDYING the current theories and experimental > record, and trying to extend one or the other. Miguel Rios- Hide quoted text - - Show quoted text - === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > The best cure for a parasite like PD is to interrupt his food source. Stop replying to the bastard! NoEinstein > Folks: My detailed explanation in my last reply to... PNG, PD, IS the > proof! Detailed explanation, my foot. Where are your *calculations*. Physics >is a *quantitative* science. If you do not do calculations, then you >are not doing physics. PD makes a good point when he points out that Physics a *quantitative* science. > If you do not do calculations, then you are not doing physics. Hopefully, rather than make unsubstantiated claims, > and attack posters who oppose Relativity, the General Relativity Cultists will begin to post calculations > rather than useless references that may or may not > support their positions. This is a pointless and inefficient exercise, and I am shocked that > you, who rail at the inefficiencies of science, would encourage such > an activity. ASCII Usenet is a horrible medium for communicating calculations, and > it would serve absolutely no purpose other than to spoonfeed you at > your chosen trough of convenience. In an efficient mode of communication, there is an optimum whereby > transmitter does some work and receiver does some work, and a system > design where the transmitter does all the work and the receiver does > none is almost guaranteed to be a wasteful method. The calculations are easily available to you, Potter, and the best > thing a relativity cultist can do to facilitate your education is to > give you directed pointers to places where you can look, rather than > you attempting a raw search yourself. One would think that if the General Relativity Gurus > and Cultists were privy to such powerful, esoteric knowledge, > that they would use their powerful knowledge > to make a few bucks in the free market. The best I can determine is that the > General Relativity Gurus and Cultists > are either phones, bullshippers, brainwashed students, > or on the public dole. -- > Tom Potterhttp://tdp1001.spaces.live.com/http://www.tompotter.us/misc.htmlhttp:. . .- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole The best cure for a parasite like PD is to interrupt his food source. > Stop replying to the bastard! NoEinstein You are getting increasingly vicious to those who point out your mistakes. You need to get some anger therapy before you get yourself into trouble. Folks: My detailed explanation in my last reply to... PNG, PD, IS the >proof! >Detailed explanation, my foot. Where are your *calculations*. Physics >is a *quantitative* science. If you do not do calculations, then you >are not doing physics. >PD makes a good point when he points out that >Physics a *quantitative* science. >If you do not do calculations, then you are not doing physics. >Hopefully, rather than make unsubstantiated claims, >and attack posters who oppose Relativity, >the General Relativity Cultists will begin to post calculations >rather than useless references that may or may not >support their positions. >This is a pointless and inefficient exercise, and I am shocked that >you, who rail at the inefficiencies of science, would encourage such >an activity. >ASCII Usenet is a horrible medium for communicating calculations, and >it would serve absolutely no purpose other than to spoonfeed you at >your chosen trough of convenience. >In an efficient mode of communication, there is an optimum whereby >transmitter does some work and receiver does some work, and a system >design where the transmitter does all the work and the receiver does >none is almost guaranteed to be a wasteful method. >The calculations are easily available to you, Potter, and the best >thing a relativity cultist can do to facilitate your education is to >give you directed pointers to places where you can look, rather than >you attempting a raw search yourself. >One would think that if the General Relativity Gurus >and Cultists were privy to such powerful, esoteric knowledge, >that they would use their powerful knowledge >to make a few bucks in the free market. >The best I can determine is that the >General Relativity Gurus and Cultists >are either phones, bullshippers, brainwashed students, >or on the public dole. >-- >Tom Potterhttp://tdp1001.spaces.live.com/http://www.tompotter.us/misc.htmlhttp:. . .- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) As can be seen from your reference > 10 General Relativistic Models for Space-time.. > and Ashby's paper that uses 13 Classical Physics hacks > of GPS data to fit it to General Relativity, unlike DNA scientists, computer scientists, electronics scientists, etc. > all of the General Relativity Gurus seem to be guys on the Public Dole, > who have never made a real world contribution to mankind. One would think that if General Relativity Gurus > possessed such powerful, esoteric knowledge, > they would use it to make a few bucks in the free market, rather than being a burden to hardworking taxpayers, > and wasting the minds and time of young folks > on issues such as time travel, worm holes, > the beginning and end of the universe, > and the mind of God. A mind is a terrible thing to waste. My, my Potter, you do try to disparage things you have FAILED > to understand, such as General Relativity and it's applications! Hey, Potter, GTR has directly contributed to a $30B+ GPS industry, > benefiting people all over the world. Aviation, shipping, asset > management, survey, mining, agriculture, time dissemination, > communications networks... and on and on! Bluster on, Potter, bluster some more! Froth at the mouth! Whatever!- Hide quoted text - - Show quoted text - Science teachers: Those who teach errors by rote and consider themselves to be learned. NoEinstein === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole <0_JMl.92445$DP1.86702@attbi_s22> posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) As I asked: > What point do all inertial observers reference the acceleration of an Observed acceleration to Potter, did you ever learn calculus or take a calculus based physics > course? Science teachers: Those who teach errors by rote and consider themselves to be learned. NoEinstein === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > In my haste to get past the riff-raff replies, I left off the following information=rich links: Where Angels Fear to Fall Last Nails in Einstein's Coffin Pop Quiz for Science Buffs! An Einstein Disproof for Dummies Another look at Einstein Three Problems for Math and Science Matter from Thin Air Curing Einstein's Disease Replicating NoEinstein's Invalidation of M-M (at sci.math) Cleaning Away Einstein's Mishmash Dropping Einstein Like a Stone Plotting the Curves of Coriolis, Einstein, and NoEinstein (is Copyrighted.) Are Jews Destroying Objectivity in Science? The Gravity of Masses Doesn't Bend Light. KE = 1/2mv^2 is disproved in new falling object impact test. Light rays don't travel on ballistic curves. A BLACK HOLE MYTH GETS BUSTED: > Folks: PD is a certifiable LUNY who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein And you are one who repeatedly redirects the argument away from proof. Show us the science. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > of my science research and analysis. It would be most helpful if you would reply and give a similar list of your posts... IF you have any. NoEinstein > Folks: PD is a certifiable LUNY who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein And you are one who repeatedly redirects the argument away from proof. Show us the science. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole of my science research and analysis. Yes, they do. The depth is zero. It would be most helpful if you > would reply and give a similar list of your posts... IF you have any. > NoEinstein Folks: PD is a certifiable LUNY who thinks that if he asks an already- >well-answered question often enough, that he will discredit my science >truths. Smart readers among you must surely understand why I consider >PD to be a persona non grata, unworthy of being given the time of >day! NoEinstein >And you are one who repeatedly redirects the argument away from proof. >Show us the science. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > Folks: Parasites like PD should be dealt with in the most drastic ways. Unfortunately, these news groups only allow the use of words. NoEinstein Folks: PD is a certifiable LUNY who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein Folks: The question which PNG, PG, keeps asking was completely > answered in this original post, as well as in several of my replies. Please provide a link to your post with the calculations. Amazing how you tend toward violent thoughts when people ask you to > show your calculations. PD- Hide quoted text - - Show quoted text - === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole Folks: Parasites like PD should be dealt with in the most drastic > ways. Unfortunately, these news groups only allow the use of words. > NoEinstein So you are advocating violence against those who point out your mistakes? That is both crazy and illegal. Folks: PD is a certifiable LUNY who thinks that if he asks an already- >well-answered question often enough, that he will discredit my science >truths. Smart readers among you must surely understand why I consider >PD to be a persona non grata, unworthy of being given the time of >day! NoEinstein >Folks: The question which PNG, PG, keeps asking was completely >answered in this original post, as well as in several of my replies. >Please provide a link to your post with the calculations. >Amazing how you tend toward violent thoughts when people ask you to >show your calculations. >PD- Hide quoted text - >- Show quoted text - === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > Folks: Parasites like PD should be dealt with in the most drastic ways. Unfortunately, these news groups only allow the use of words. NoEinstein Folks: The question which PNG, PG, keeps asking was completely > answered in this original post, as well as in several of my replies. Can't find any calculations anywhere in your posts, NoEinstein. Where > are they? Are you a liar? Only a FOOL, like PD, would keep asking a question that has already > been well answered. NoEinstein only corrections for the varying ether density and flow near the > Earth. Because both of the latter conform to the inverse square law, > Einstein's empirical GR equations are a close analogy to my actual > ether flow and density... SCIENCE. The advantage of the latter is > that such is the mechanism causing gravity, and doesn't require > bastardizing space-time on the whim of a (barely) moron Albert > Einstein. NoEinstein Well, John, the proof of the pudding is in the eating. > You say the correction isn't due to relativity but to varying ether > density. One is the true prince, and the other is an impostor. And > here is how science tells the difference: > - The true prince will be able to tell you how big a correction to > make *in advance*, and when the correction is made, it will work. > - The impostor will not be able to generate a calculated correction > *in advance* and will only claim the answer after the fact. Now, if you think the varying ether density model is the true prince, > then the test before you is simple. Show the calculation that > generates the correct correction for an orbit of arbitrary altitude H. > Relativity can do that. Can you? PD- Hide quoted text - - Show quoted text - === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > Folks: Parasites like PD should be dealt with in the most drastic ways. Unfortunately, these news groups only allow the use of words. NoEinstein Folks: PD is a certifiable LUNY who thinks that if he asks an already- > well-answered question often enough, that he will discredit my science > truths. Smart readers among you must surely understand why I consider > PD to be a persona non grata, unworthy of being given the time of > day! NoEinstein Don't you think it's remarkable that I ask you for your calculations, > and all of a sudden you have conniptions? Do you consider anybody that would ask you for your calculations to be > a personal non grata? Everybody else does in physics. Why are you exempt? === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=vAXmIgoAAAAc1JqsgUNMfUUawhdjr9Jp SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) >.com>, > However, if I haven't dropped a decimal place somewhere, I'm getting t= >hat > a satellite in Jovian synchronous orbit would run slow by about > 150 microseconds/day due to SR. =3DA0GR I'm leaving to someone else. You can claim half a credit... =A0if you show us your calculations. Oh for crying out loud. =A0I couldn't look up what a jovisynchronous > orbit would be (stupid Wikipedia), but simple Newtonian mechanics > gives 160,795km from the center and a velocity of about 28km/sec > (which compares favorably with the values from Jupiter's natural > satellites, so I can't be that far off). =A0Then just plug that into > the Lorentz equation. >The task was to compute the offset predicted by GR for JPS >satellites. You computed the SR offset. Talk about a reading >disability... Actually you asked for the offset predicted by relativity. I > provided part of the calculation. I still have no idea what you > expect to get from the result. A little bit of research dug up the equation for time dilation due > to GR, but I can't be bothered to do the math because, hey, I'm not > the one with a bug up my ass about it. FWIW T = T 0 / sqrt(1-(2GM)/Rc^2) As folks familiar with physics history know, > Galileo experimented with oscillating systems and accelerations centuries ago, > and discovered that the frequency of an oscillating system > is affected by the Earth's acceleration. >I think it is so funny that you still don't know what the you are >talking about despite bringing this point up nearly every ing >time you to to make GR look stupid. >Learn the difference between a pendulum and an oscillator, tool. > I am pleased to see that my high school graduate pal Gisse, > considers me a tool he can use to educate himself in physics, > and I am pleased to see that Gisse wants to know > the difference between a pendulum and an oscillator. > oscillator: > a device or machine producing oscillations > oscillations: > Repeating fluctuations in a physical object or quantity. > As can be seen > as a pendulum is an oscillator, > there is no difference. > I am pleased that I could be the tool > to educate Gisse in this matter. > -- > Tom Still osculating the pendulum, Tom? Double-A Better to osculate the pendulum, the mechanical system that > ushered in modern physics and philosophy, by providing man with an oscillating system, > that took the focus off of Moon and Sun GODS , and put it on MAN made systems that oscillated, and could be used to investigate finer and finer > time units, and understand NATURE more completely, than to osculate General Relativity, > a model that wastes time, money and minds by returning man to ancient auguring models of reality, > that pretend to model things beyond the capacity of man > to ever experience in time and space, like the beginning and end of the universe, > and the mind of God. A mind is a terrible thing to waste. -- > Tom Potter > http://tdp1001.spaces.live.com/ > http://www.tompotter.us/misc.html > http://www.geocities.com/tdp1001/index.html > http://notsocrazyideas.blogspot.com > http://www.flickr.com/photos/tom-potter/ > http://tdp1001.wiki.zoho.com > http://groups.msn.com/PotterPhotos The MSN Groups service has closed As we first announced on October 23 2008, the MSN Groups service has closed. If you would like to create a new group, we have established a partnership with Multiply - an online group and media sharing service that is tailored to the needs of larger groups. If you would like to create a small group of less than 1000 members, please visit Windows Live Groups. For further information on the closure of MSN Groups, please access one of the following local blogs: US | Deutschland | UK | Espa.96a | Mexico | France | Italia | .93.9c.96{ | Nederland | Brasil > http://www.androcles01.pwp.blueyonder.co.uk/dingleberry.htm Double-A === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=sVBCDQoAAAADe-Ogi2R38m91EmLrcIgt Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) >Real scientists do not do, nor report, their research on this forums. >They study the subjects, they make measurements and simulations and, >finally, report their findings in conferences and journals (that is at >least what I do). Talking of real people doing science, and working in real problems, >here are some references to read: 1) 10 General Relativistic Models for Space-time Coordinates and >XXVIIA Reports on Astronomy 2006-2009, pp55-59. >Tou Ni, Michael C.W. Sandford, Christian Veillet, An-Ming Wu, Patricia >Fridelance, Etienne >Samain, George Spalding and Xiaohui Xu, Adv. Space Res. Vol. 32, No. >4) Relativistic Corrections to Lunar Occultations, Costantino >Sigismondi, Tenth Italian-Korean Meeting on Relativistic Astrophysics >Pescara, June 25-30, 2007. >5) Deep-space laser-ranging missions ASTROD and ASTROD I for >astrodynamics and astrometry, W. T. Ni and the ASTROD I ESA COSMIC >Astrometry Proceedings IAU Symposium No. 248, 2007. Miguel Rios I was not Talking of real people doing science, > I was Talking of real people doing REALITY. As can be seen from your reference > 10 General Relativistic Models for Space-time.. > and Ashby's paper that uses 13 Classical Physics hacks > of GPS data to fit it to General Relativity, unlike DNA scientists, computer scientists, electronics scientists, etc. > all of the General Relativity Gurus seem to be guys on the Public Dole, > who have never made a real world contribution to mankind. One would think that if General Relativity Gurus > possessed such powerful, esoteric knowledge, > they would use it to make a few bucks in the free market, rather than being a burden to hardworking taxpayers, > and wasting the minds and time of young folks > on issues such as time travel, worm holes, > the beginning and end of the universe, > and the mind of God. A mind is a terrible thing to waste. -- > Tom Well Mr. potter, regarding the chicken situation, I'm quite sure you > do not need Galileo, Newton, nor Einstein theories to find your way to > your bathroom at night. That is how reality works!!. Science, on the other hand, has always worked differently to that. You > observe Nature and wonder how and why it works like like you see it. > Then you build a model that may, or may not, be useful to predict the > results of observations. Many advances on physics or mathematics take > several years to understand, and then more years to get into real > useful applications of those new advances. One example: in the early > 60's, Dr. Robert Gallager, on his Ph.D. thesis, found a mathematical > method that could be used in coding systems. The method is called Low > Density Parity Check (LDPC). For over 30 years nothing happened with > his development (even him had forgotten it), until somebody found the > method could be applied to the 3G and 4G cellular systems. So now, > almost all cellular systems are using these LDPC codes to improve the > quality of communications. Furthermore, History has shown that nobody has ever developed a new > and useful theory without being familiar with the then-current > theories and experiments. That's why the idiots and crackpots around > here are so pathetic: if they truly wanted to make a contribution, > they would be seriously STUDYING the current theories and experimental > record, and trying to extend one or the other. Miguel Rios Seriously studying SRT has led to some serious doubts, by some very knowledgeable people : -The person who invented the atomic clock -A scientist who had a big hand in developing GPS Those of us who know basic algebra and have done College level physics also have a hard time reconciling the various contradictions within SRT- after years of study and discussion. A person on a moving train or a person on a platform beside the moving train will see lighting flashes simultaneously since the points of origin of the lightning is a fixed distance from that person in both cases. If light is measured the same regardless of movement of source or observer. So there is no relativity of simultaneity. There are many such miracles in SRT. But if all the miracles he performed were written down there would not be enough books in the world to contain them. These are written that ye may believe. Believe in the light also believe in the speed of light, the same yesterday today and forever in all places and all times forever and ever amen. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=hbYmMgkAAADthgUY8i5E5MN4qZlh2_fb Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) Furthermore, History has shown that nobody has ever developed a new > and useful theory without being familiar with the then-current > theories and experiments. That's why the idiots and crackpots around > here are so pathetic: if they truly wanted to make a contribution, > they would be seriously STUDYING the current theories and experimental > record, and trying to extend one or the other. Miguel Rios Seriously studying SRT has led to some serious doubts, by some very > knowledgeable people : -The person who invented the atomic clock > -A scientist who had a big hand in developing GPS Those of us who know basic algebra and have done College level physics > also have a hard time reconciling the various contradictions within > SRT- after years of study and discussion. A person on a moving train or a person on a platform beside the moving > train will see lighting flashes simultaneously since > the points of origin of the lightning is a fixed distance from that > person in both cases. If light is measured the same regardless of > movement of source or observer. So there is no relativity of > simultaneity. There are many such miracles in SRT. But if all the miracles he > performed were written down there would not be enough books in the > world to contain them. These are written that ye may believe. Believe > in the light also believe in the speed of light, the same yesterday > today and forever in all places and all times forever and ever amen. Big words G, but zero content. Like wacko Seto uses to say assertion is not proof. So if you can proof your assertion there is no relativity of simultaneity, at least Seto would be very interested. For my part, I have provided here written proof and examples of the relativity of simultaneity several times before, and you may well learn a bit from those posts. Miguel Rios === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole >Real scientists do not do, nor report, their research on this forums. >They study the subjects, they make measurements and simulations and, >finally, report their findings in conferences and journals (that is at >least what I do). >Talking of real people doing science, and working in real problems, >here are some references to read: >1) 10 General Relativistic Models for Space-time Coordinates and >XXVIIA Reports on Astronomy 2006-2009, pp55-59. >Tou Ni, Michael C.W. Sandford, Christian Veillet, An-Ming Wu, Patricia >Fridelance, Etienne >Samain, George Spalding and Xiaohui Xu, Adv. Space Res. Vol. 32, No. >4) Relativistic Corrections to Lunar Occultations, Costantino >Sigismondi, Tenth Italian-Korean Meeting on Relativistic Astrophysics >Pescara, June 25-30, 2007. >5) Deep-space laser-ranging missions ASTROD and ASTROD I for >astrodynamics and astrometry, W. T. Ni and the ASTROD I ESA COSMIC >Astrometry Proceedings IAU Symposium No. 248, 2007. >Miguel Rios > I was not Talking of real people doing science, > I was Talking of real people doing REALITY. > As can be seen from your reference > 10 General Relativistic Models for Space-time.. > and Ashby's paper that uses 13 Classical Physics hacks > of GPS data to fit it to General Relativity, > unlike DNA scientists, computer scientists, electronics scientists, > etc. > all of the General Relativity Gurus seem to be guys on the Public Dole, > who have never made a real world contribution to mankind. > One would think that if General Relativity Gurus > possessed such powerful, esoteric knowledge, > they would use it to make a few bucks in the free market, > rather than being a burden to hardworking taxpayers, > and wasting the minds and time of young folks > on issues such as time travel, worm holes, > the beginning and end of the universe, > and the mind of God. > A mind is a terrible thing to waste. > -- > Tom > Well Mr. potter, regarding the chicken situation, I'm quite sure you > do not need Galileo, Newton, nor Einstein theories to find your way to > your bathroom at night. That is how reality works!!. > Science, on the other hand, has always worked differently to that. You > observe Nature and wonder how and why it works like like you see it. > Then you build a model that may, or may not, be useful to predict the > results of observations. Many advances on physics or mathematics take > several years to understand, and then more years to get into real > useful applications of those new advances. One example: in the early > 60's, Dr. Robert Gallager, on his Ph.D. thesis, found a mathematical > method that could be used in coding systems. The method is called Low > Density Parity Check (LDPC). For over 30 years nothing happened with > his development (even him had forgotten it), until somebody found the > method could be applied to the 3G and 4G cellular systems. So now, > almost all cellular systems are using these LDPC codes to improve the > quality of communications. > Furthermore, History has shown that nobody has ever developed a new > and useful theory without being familiar with the then-current > theories and experiments. That's why the idiots and crackpots around > here are so pathetic: if they truly wanted to make a contribution, > they would be seriously STUDYING the current theories and experimental > record, and trying to extend one or the other. > Miguel Rios Seriously studying SRT has led to some serious doubts, by some very > knowledgeable people : -The person who invented the atomic clock > -A scientist who had a big hand in developing GPS Those of us who know basic algebra and have done College level physics > also have a hard time reconciling the various contradictions within > SRT- after years of study and discussion. A person on a moving train or a person on a platform beside the moving > train will see lighting flashes simultaneously since > the points of origin of the lightning is a fixed distance from that > person in both cases. If light is measured the same regardless of > movement of source or observer. So there is no relativity of > simultaneity. There are many such miracles in SRT. But if all the miracles he > performed were written down there would not be enough books in the > world to contain them. These are written that ye may believe. Believe > in the light also believe in the speed of light, the same yesterday > today and forever in all places and all times forever and ever amen. > The sad part is that it detracts from progress. Nobody is funding superluminal interplanetary communication, without which we cannot talk to the rovers Spirit and Opportunity on Mars in a reasonable time. A manned mission to Mars when it takes an hour to get a reply is a poor deal. Eventually it will happen, but the reason it hasn't already is blind faith in Einstein by the great unwashed, and they have the money. The paper shuffler Miguel Rios calls himself a real scientist but all he has to offer is make measurements and simulations and, finally, report their findings in conferences and journals. The real engineer doesn't read that crap, he gets on with it. Necessity is the mother of invention. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > My, my Potter, you do try to disparage things you have FAILED > to understand, such as General Relativity and it's applications! > Hey, Potter, GTR has directly contributed to a $30B+ GPS industry, > benefiting people all over the world. Aviation, shipping, asset > management, survey, mining, agriculture, time dissemination, > communications networks... and on and on! > Bluster on, Potter, bluster some more! Froth at the mouth! Whatever! As can be seen by Sammy's post, > General Relativity is more a religion, > than a useful model. > Hey, Potter, GTR has directly contributed to a $30B+ GPS industry, benefiting people all over the world. Aviation, shipping, asset management, survey, mining, agriculture, time dissemination, communications networks... and on and on! Bluster on, Potter, bluster some more! Froth at the mouth! Whatever! === Subject: Tom Potter is barking up the wrong tree. TomPotter is barking up the wrong tree. There are 7 billion horny people on this planet. No amount of energy or money would satisfy them. Eating more is living faster, dying sooner. LifeSpan is a function of oxygen consumption per pound. There are deeper questions. What's the origin of the species and the cosmos ? What fuels life ? how will life adapt ? === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > Potter, did you ever learn calculus or take a calculus based physics course? I am flattered to see that Sam Wormley, > is interested in me personally, > as he is in most of the thinkers in sci.physics > whose posts do not parrot conventional wisdom. A sci.physics poster knows that he is posting bullet proof posts, > when Sammy, Gisse,and Uncle Al attack the messenger, > rather than address the message in a rational, intelligent way, > and when PD does the Ali Shuffle. Bu to get back to physics and the message: > What point do all inertial observers reference the acceleration of an Observed acceleration to? It appears to me that Sammy thinks that Observed acceleration is calculus > rather than an observed/measurable physical property. > Calculus is not part of your education apparently, Potter. Hence, I should not expect you to have a grasp of acceleration being defined at dv/dt.... nor an understanding of its meaning in a physical context. As I often ask poster, velocity with respect to what? as velocity with respect to what. Potter thought he was being clever asking acceleration with respect to what? without any physical understanding. Bluster on, Potter, bluster some more! Froth at the mouth! Whatever! === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole <0_JMl.92445$DP1.86702@attbi_s22> posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > have used calculus to solve, or help to solve, a single daunting problem. Unless you can cite the latter, then your insistence that calculus be part of Potter's proofs is all bluster and no substance. You are an academiac who embraces education for education's sake. And such attitudes are effectively bringing down this country. Barack Obama is so naive that he believes that all minorities should get college educationspaid for by government. Unfortunately, quality jobs don't get created, automatically, to allow the (dumb) college educated to go through life without doing any physical labor. Instead of MORE education, public education should stop at age 16, and no public money should be used to send anyone to college, anywhere. We need to restore the work ethic in the USA, not destroy the remaining vestiges by sending more than 15% of the top high school graduates to college. NoEinstein > Potter, did you ever learn calculus or take a calculus based physics course? I am flattered to see that Sam Wormley, > is interested in me personally, > as he is in most of the thinkers in sci.physics > whose posts do not parrot conventional wisdom. A sci.physics poster knows that he is posting bullet proof posts, > when Sammy, Gisse,and Uncle Al attack the messenger, > rather than address the message in a rational, intelligent way, > and when PD does the Ali Shuffle. Bu to get back to physics and the message: > What point do all inertial observers reference the acceleration of an Observed acceleration to? It appears to me that Sammy thinks that Observed acceleration is calculus > rather than an observed/measurable physical property. Calculus is not part of your education apparently, Potter. > Hence, I should not expect you to have a grasp of acceleration > being defined at dv/dt.... nor an understanding of its meaning > in a physical context. As I often ask poster, velocity with respect to what? as velocity > with respect to what. Potter thought he was being clever asking > acceleration with respect to what? without any physical understanding. Bluster on, Potter, bluster some more! Froth at the mouth! Whatever!- Hide quoted text - - Show quoted text - === Subject: I solved it. posting-account=TwCTWQgAAAC7hf6GV7aTGIk6mVGkiZ5c FDM),gzip(gfe),gzip(gfe) > DId anyone here see the problem presented in > the Science section of NY Times last week? > Quite startling, to see something so sophisticated > in a 'general readership' publication. Is it solvable without a calculus of variations approach? I solved it using brain No Calculus needed. Bye Sanny Enjoy & Chat: http://www.GetClub.com === Subject: Re: I solved it. DId anyone here see the problem presented in > the Science section of NY Times last week? > Quite startling, to see something so sophisticated > in a 'general readership' publication. Is it solvable without a calculus of variations approach? I solved it using brain No Calculus needed. Me too. I just shot the damn thing. Then a 'gator ate it. -- You can't have a sense of humor, if you have no sense! === Subject: Re: Expanding space and The Universe's age Tell me, is the universe infinite and unbounded, finite and bounded, > infinite and bounded or finite and bounded. Can you even tell me what > consequences each of these postulates have for any model of the > universe? Oh wait... why am I even bothering to ask you, as you have no > clue. > If we're talking about size, then that means we are talking about > measurements of length, relative space. Relative space certainly doesn't appear to be infinite. Obler's Paradox sort of neatly decides that issue. I think asking about the size of the Universe is a ridiculous question. Feel glad the universe does not care what you think... especially about its size. *smirk* === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > Tell me, is the universe infinite and unbounded, finite and bounded, > infinite and bounded or finite and bounded. Can you even tell me what > consequences each of these postulates have for any model of the > universe? Oh wait... why am I even bothering to ask you, as you have no > clue. If we're talking about size, then that means we are talking about > measurements of length, relative space. Relative space certainly doesn't appear to be infinite. Obler's Paradox sort of neatly decides that issue. I think asking about the size of the Universe is a ridiculous question. Feel glad the universe does not care what you think... especially about > its size. *smirk*- Hide quoted text - - Show quoted text - Why are you afraid of a size? The universe has one but we can't see it because it is ahead in our time. We have to wait light years to see the future of something distant. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age <5b796$4a05e919$cdd08502$10688@DIALUPUSA.NET> posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) >On May 9, 11:26 am, Ahmed Ouahi, Architect What happens first is not necessarily the beginning. There is nothing before the beginning of time. >So when did it begin? How long ago? If I told you how would you know it was right? >The real point of the question was how do you know >there was a beginning? Since you cannot identify >when you also cannot reasonably infer there was >a beginning. But you can infer that time has existed >in the past because it exists now. Anything past the >next tick is up for grabs.- Hide quoted text - >- Show quoted text - Why do you question it? Space-time shrinks back to zero. It appears to you to do so. That is a very poor > foundation for your pronouncement.- Hide quoted text - - Show quoted text - The universe shrinks to a beginning if you move back in time. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age >On May 9, 11:26 am, Ahmed Ouahi, Architect What happens first is not necessarily the beginning. There is nothing before the beginning of time. >So when did it begin? How long ago? If I told you how would you know it was right? >The real point of the question was how do you know >there was a beginning? Since you cannot identify >when you also cannot reasonably infer there was >a beginning. But you can infer that time has existed >in the past because it exists now. Anything past the >next tick is up for grabs.- Hide quoted text - >- Show quoted text - Why do you question it? Space-time shrinks back to zero. It appears to you to do so. That is a very poor > foundation for your pronouncement.- Hide quoted text - - Show quoted text - The universe shrinks to a beginning if you move back in time. Mitch Raemsch ****************************************** Agree. If time always existed, then you would have to count to infinity to get to today. Herc === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) On May 9, 11:26 am, Ahmed Ouahi, Architect What happens first is not necessarily the beginning. There is nothing before the beginning of time. >So when did it begin? How long ago? If I told you how would you know it was right? >The real point of the question was how do you know >there was a beginning? Since you cannot identify >when you also cannot reasonably infer there was >a beginning. But you can infer that time has existed >in the past because it exists now. Anything past the >next tick is up for grabs.- Hide quoted text - >- Show quoted text - Why do you question it? Space-time shrinks back to zero. It appears to you to do so. That is a very poor > foundation for your pronouncement.- Hide quoted text - - Show quoted text - The universe shrinks to a beginning if you move back in time. Mitch Raemsch ****************************************** Agree. If time always existed, then you would have to count to infinity to get to today. Herc- Hide quoted text - - Show quoted text - It has an absolute beginning. === Subject: Stochastic integral posting-account=frVNsgoAAADqMe0QlqRY45SfNlclErPW AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) I don't fully understand the following result: Let H=sum_k (Z_k Ind_{ (T_k,T_{k+1}] }) be a simple process. That is, an infinite sum of F_{T_k}-measurable uniformly random variables Z_k multiplied by indicators of half-open intervals between a sequence of stopping times T_k and T_{k+1}. Also let M be a cadlag martingale bounded in L^2. There is a norm, denoted N below, which I'm told is the square of the norm of M in the space of [Cadlag martingales bounded in L^2]. And E denotes expectation. Proposition states the following are equal - N (H.M)^2 - E ((H.M)_infty^2) - sum_k E(Z_k^2 (M_{T_{k+1}}^2 - M_{T_k}^2)) and these are all leq than - norm(H)_infty^2 N(M)^2. I am really confused about these quantities, help please!! === Subject: Unscented transformation Hi all. I'm trying to understand the unscented transformation with respect to the unscendted kalman filter. I think I have understood the basic idea, but I have some troubles with the definition of the sigma points. I quote from Unscented Filtering and Nonlinear Estimation by Julier and Uhlmann: A set of sigma points are chosen so that their mean and covariance are x_bar and Sigma_x . The nonlinear function is applied to each point, in turn, to yield a cloud of transformed points. The statistics of the transformed points can then be calculated to form an estimate of the nonlinearly transformed mean and covariance They then give an example of a symmetric set of sigma points that lie on the sqrt(N)'th covariance contour. The sigma points are then given by rows of the square root matrix of N*Sigma_x for example calculated from the Cholesky decomposition. My questions are: What do they mean by the sqrt(N)'th contour? Why do they choose the sqrt(N)'th covariance contour? Do they mean the set of points where the mahalanobis distance of x equals sqrt(N)? In other words where (x - x_bar)^T * Sigma_xÂ^-1 * (x - x_bar) = sqrt(n)? If this is the case, why is this set of points given by the square root matrix? === Subject: Re: Unscented transformation posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) > Hi all. I'm trying to understand the unscented transformation with respect to the > unscendted kalman filter. I think I have understood the basic idea, but I > have some troubles with the definition of the sigma points. Just a suggestion. You might want to consider posting this question on one of the stat ngs (like sci.stat.edu and sci.stat.math) and also to the electrical engineering or digital signal processing ngs (like comp.dsp). These people might have more experience with Kalman filters than the folks in the strictly math ngs. Good Luck, Matt === Subject: Two times for matter one time for light posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) Matter obeys SR and GR. Light does not change motion therefore it is only effected by GR. Matter is a form of two energies. Infinitely dense point energy and finite dense energy of force surrounding that point. Mitch Raemsch === Subject: Re: Timing of GCD algorithms > [...] I am working > on something which involves the timing of various GCD(m,n) algorithms. > If memory serves right the worst case for the Euclidian algorithm is > O(m^2*n^2) bit operations [...] > Suppose I have a certain function S(Euclid(m,n)), with S being the > actual steps of the Euclidian algorithm for finding the GCD for all > (m,n) in {1,2,3,...,N} x {1,2,3,...,N}, for some natural N, with > Euclid's algorithm. > My question: is the function S(GCD(m,n)), where GCD(m,n) are various > other (perhaps more efficient) GCD algorithms 'similar' to > S(Euclid(m,n)) in its overall behavior? The way you've defined S, S(Euclid(m,n)) is identical to S(x), > where x is anything whatsoever. Perhaps you want S(G, K) to be > a function from A x N to N whose value is the number of steps for > method G to compute gcd(i,j) for all i in {1..K}, j in {1..K}, > with N being the set of natural numbers and A the class of GCD > algorithms. A much better description, thank you! My apologies for taking so long to reply, I am still thinking about this problem and I am going nowhere fast, because my infinite stupidity is making attempts to resurrect itself, as of late :-) > That aside, are you timing GCD algorithms to find out which is faster, > and wish to find best case, worst case, average case, or other, stats? Here's what I hope is a more concise form of my question: The performance of Euclid's algorithm for GCD (in terms of total steps taken) is shown on the following wiki page: http://en.wikipedia.org/wiki/Euclidean_algorithm (section algorithmic efficiency, blue-yellow graph) According to your much better definition, this is the performance graph for S(Euclid, K), with K ~ 300. My question is: Is the performance graph for S(G,K), for G =/= Euclid, similar to that of S(Euclid,K) shown in wiki? If I understand my own question well enough, I think that the actual O(time) of the involved algorithm is probably irrelevant to my question, because such a graph measures the number of steps only relative to the total number of steps for the algorithm. -- Ioannis --- There's _always_ a mistake, somewhere. === Subject: Re: K-12 Calculator Woes >On 6 May 2009 15:02:53 -0400, hrubin@odds.stat.purdue.edu (Herman >What mathematics do non-mathematicians need? They need >to understand the mathematical concepts which will be >used in their work, and for most this will need an >understanding of the real numbers and limits. They >need to be able to use mathematical notation to >translate their real-world problems into mathematical >representations which then can be solved by mathematical >methods. What they will not be able to do, except in >very simple situations, is carry out the solution. >Herman, most non-mathematicians in non-technical fields do NOT use >these concepts at all. The use of technical fields is expanding, and even those in non-technical fields could make good use of the concepts to simplify their calculations. Furthermore, if they have not seen the concepts, and have even moderate difficulty with the manipulations, they may well not enter a technical field. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes > The representation of fractions is, for a machine, much > harder than floats or decimals, and is more complicated > to work with. >Why do you believe that is true? Fractions, unless their size is limited, will require at least two words, and their operations are more complex. Machines rarely do exact arithmetic, as would be required with fractions to give the answers desired. Avoiding computer roundoff would be expensive. I am reasonably familiar with computer architecture, and I can see no way around it. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes posting-account=9tP_uwoAAAD1vfWhLdsNH4ImDfm7cP1K 4337.29; Windows NT 5.1; GTB6; .NET CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) spider-mtc-ta01.proxy.aol.com[400C7001] (Prism/1.2.1), HTTP/1.1 cache-mtc-ae12.proxy.aol.com[400C7510] (Traffic-Server/6.1.5 [uScM]) piece by Frank Quinn, K-12 Calculator Woes, at: >http://www.ams.org/notices/200905/rtx090500559p.pdf The real problem is that learning arithmetic from rules > is the same as learning reading without phonics. ?A > mathematician does not have to be adept at arithmetic; > how many are we losing this way? We CAN teach the structure and conceptS; yes, there is > more than one concept of the integers. ?The two major > ones are the cardinal and the ordinal, and the original > new math people seemed stuck on the cardinal, which looks > easy, but that is deceptive. ?The ordinal one can be > understood by children quite easily, and one can build > from it, including putting in the cardinal one. Children should not memorize addition and multiplication > tables, but should build them themselves. ?The teaching > of anything by memorization and routine hinders and even > may destroy understanding. There is no sour grapes in this; I probably use mental > arithmetic too much. ?Not only here but elsewhere I > have found concepts to be hard to get at given computation > or weaker concepts, but easy to understand once found, > and even easy to teach to those not prejudiced. -- > This address is for information only. ?I do not claim that these views > are those of the Statistics Department or of Purdue University. > Herman Rubin, Department of Statistics, Purdue University > hru...@stat.purdue.edu ? ? ? ? Phone: (765)494-6054 ? FAX: (765)494-0558 Herman; As I recall, Purdue has a selective enrollment. I teach at an open enrollment state university. In the past (say 10-15 years ago), incoming freshmen engineers knew a reasonable amount of arithmetic, algebra and trigonometry, so that we could at least get them to learn the rote calculations in calculus, and sometimes learn how to actually formulate and use the same ideas. Now, they stumble over simplifying 2 (3x), let alone 3(3^n) or sqrt(9). In terms of your idea of teaching the background, how would it be to teach english without any spelling or grammar, except that provided by Word (TM)? Do you realize how slow everyone would be? === Subject: Re: K-12 Calculator Woes >: >.com>, >piece by Frank Quinn, K-12 Calculator Woes, at: >http://www.ams.org/notices/200905/rtx090500559p.pdf >Herman; >As I recall, Purdue has a selective enrollment. I teach at an open >enrollment state university. In the past (say 10-15 years ago), >incoming freshmen engineers knew a reasonable amount of arithmetic, >algebra and trigonometry, so that we could at least get them to learn >the rote calculations in calculus, and sometimes learn how to actually >formulate and use the same ideas. Now, they stumble over simplifying 2 >(3x), let alone 3(3^n) or sqrt(9). The Purdue enrollment is not that selective, and this is still likely to arise. Do you think the Indiana high schools teach any better than yours? One of my colleagues told me about a minority student having difficulties; nobody had ever indicated to him that HE could formulate word problems. >In terms of your idea of teaching the background, how would it be to >teach english without any spelling or grammar, except that provided by >Word (TM)? Do you realize how slow everyone would be? I do not know how badly it is done now, but the linguists' idea of teaching a foreign language is to do it orally, with minimal emphasis on the written language. American school children are not held to much spelling, and in some places, grammar is absent. I would teach the principles of the language, which definitely include the grammar, or enough of it to logically develop the rest, and similarly for spelling, although here there are lots of exceptions. I would not do it word by word, as is commonly done. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes > They unanimously put forward the existence of > calculators to do the calculations, and calculators use decimals There are calculators that *do* other fractions. When I was teaching > the lower math classes in high school, these were often used so the > kids never had to do any fractions at all aside from entering them > into calculators. http://wize.com/calculators/t61953-fractions When I taught these were too expensive. We had to standardize models --- imagine having to support 5 different types! It was a poor community and the school had to supply many devices for the poorest,and keep prices down for the rest. Besides, manipulating rationals on a calculator only requires pushing a couple more buttons. Larry === Subject: Re: K-12 Calculator Woes > They unanimously put forward the existence of > calculators to do the calculations, and calculators use decimals > There are calculators that *do* other fractions. When I was teaching > the lower math classes in high school, these were often used so the > kids never had to do any fractions at all aside from entering them > into calculators. > http://wize.com/calculators/t61953-fractions >When I taught these were too expensive. We had to standardize models --- >imagine having to support 5 different types! I know of several $5 calculators which have fractions. >It was a poor community and the school had to supply many devices for >the poorest,and keep prices down for the rest. >Besides, manipulating rationals on a calculator only requires pushing a >couple more buttons. >Larry -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes ................ Knowing how to do arithmetic is useful, but not > essential. Understanding the numbers, and I do not > mean strings of numerals, is essential, and most of > our high school teachers of mathematics do not have > any of that. > Using calculators removes students from the numbers, hindering > understanding. No, it does some removing students from operators > with sequences of numerals. The understanding does > not at all come from familiarity with arithmetic, > but in understanding numbers as such. > And calculators remove the need to understand numbers, replacing that > understanding with an understanding of programming calculators. Understanding numbers is NOT understanding strings of > decimal digits. There are two main concepts for the > integers, and neither of them has anything to do with > the decimal representation. The decimal representation is only ONE way of representing > numbers; it is sometimes not even useful. > For 99% of he population it is the only way of representing and > manipulating numbers. Even rational fractions disappear from their > lexicon for most, unless they user a tool like a tape measure. Heck, > even fractions have virtually disappeared from he stock market. There are other means as well. Those in the sciences, and > in many other fields as well, misuse mathematics because > they have learned procedures which require assumptions to > be met to be valid. > You continue to miss the point. Yes, there are other methods, like base 16 for carpentry using caricatures of tools instead of letters and numerals because studs are 16 inches on center. But for those out there in the real world other methods do not exist, either because they are unaware of them, because their technology cannot handle them, or they just plain flat out refuse to acknowledge their existence. Why us a base 16 measuring system when the base 10 is perceived to be better, the technology is designed around that system and they already know it? Does any other system work better. Absolutely no!. Talk a bout wasting time and effort! > They have NOT. The string 6.43 means 6 plus 43/100. If they > do not understand the decimal fractions are fractions, they do > not understand decimal fractions. > I said the rational representation of fractions. I agree that not enough is done with this, and that > computers have a lot to do with the problem. It is > easy to get computers to run in base 2 arithmetic, > including for real numbers, and even the important > fixed-point arithmetic is difficult on them. The > representation of fractions is, for a machine, much > harder than floats or decimals, and is more complicated > to work with. However, the teaching of fractions leaves even more > to be desired. In can be made both rigorous and > more simple. Of course, anything is simpler if one > has algebraic notation, by which I mean that a > variable is a symbolic expression which can stand > for anything. So we have, for h not 0, a/b = ah/bh, and if the idea of fractions is presented with a > modicum of intelligence, it is obvious that a/b + c/b = (a+c)/b. > I don;t know about your school district, but that is part of my districts middle school curriculum. You suggest that 6 yr olds can handle this. I disagree, and most other s do, too, because most 6 yr old have not reached the mental stage to understand representation. They are still in a concrete world. I also agree with you that too many early ed teachers lack the math understanding to teach this. But that is slowly changing as a ndew crop of teachers enters the schools. I, for ex, was he first math certified teacher in my middle school, the others were gen ed. 4 years later all 4 8th grade math teachers are math certified (i'm gone). > Because of calculators people do not use that form, and they cannot > manipulate them, and often cannot understand them. My concern is that they understand them, and hence > can properly use them. > My experience is they have no idea how hey work, they are magic black boxes. Even worse, they have no interest in understanding how they work, even to the point that they refuse to even try. Starting in the 4th grade. Why bother to understand how a tv works? Push certain buttons and good things happen. Or a pc, microwave, elevator, or cell pone. Most don;t care until they break, then they go to an expert to fix it, or even worse, throw the broken one away and get a new one. > That 99% thinks that the decimal representations ARE the > numbers, and have no ideas of the properties of numbers. > They have no need to know more. They certainly do; that is the problem. Once they > get that attitude, it becomes very difficult to > teach them the concepts. > That attitude develops i elementary school usually through parental adn peer input. And for most of wht they do, it is enough. I agree, more is needed, at the very least a grounding in logic that induction can give. When when technology can do it , why bother? > If they think a representa tion is the thing represented, at > best they are confused. It is like the following non-paradox: One cat has one more tail than no cat. > No cat has eight tails. > Therefore, one cat has nine tails. How can you be so confident? We are turning out far too > many people who do not understand what they are doing, using > routine procedures which have assumptions which are not stated > and which are usually not correct. > You totally misunderstand me. > I am not confident, I am appalled. As am I. > But I think your position is far too much of a swing of the pendulum Concepts and even proofs are easy if properly done. I'd love to see this. I never have. I have had claases taught by or attended by geniuses who get it. But I and others, including some of my professors, had to work hard to get many concepts. For most many concepts are beyond their early understanding. New math, for ex., code for set theory, make s little sense in the early years as concepts of members, union, intersection, subsets, complement,and such are taught. Bt those concepts, as you well know, are critical for an understanding of continuity, I doubt 9th grade algebra class could grasp continuity even in a semi-formal manner, but hey cn grasp new math. But, as seen in this forum, society hates new math,and they, who pay the bills, are trying to get rid of it. They do this in part because they see no use for it. Absolute value is a fairly easy concept to grasp, but until ut is expanded to a neighborhood and used to prove a set is closed, etc., it has little real world connection Systems of linear equations mean little at the 2x2 or 3x3 level taught in schools. But when you get to optimization and solve a system of 22 equations in 31 variables (and yes, at first we did the simplex tables by hand) , you can relate to the concept. > I have seen another with the same idea of an introductory > approach to the integers, namely, use a notation which > is clumsy for computation, but excellent for understanding, > which is 0 followed by a string of tick marks. With this, > one can introduce from the Peano Postulates addition as a > moving of tick marks, etc. The associative law of addition > is a simple example of the use of the axioms. Also, one > can introduce the cardinal concept as moving the whole > bunch of tick marks at the same time. And the same thing can be, and is taught with arabic numerals. The reflexive, symmetric, and transitive properties are taught at early levels. All the texts I've seen also use alternative symbols like fruit, geometric shapes, and animals to reinforce the concepts. > I have repeatedly stated that math skills for students need to be > improved, and that the very first step in that improvement is the > removal of calculators from the classroom. I agree that the skills are USEFUL, and should not be > discouraged. I practice my computational skills. > Calculators, and computers, have changed attitudes int he public away >from the need to understand basic mathematical concepts, and the > rational representation of fractions is a perfect example. Some calculators have rational capabilities, somewhat limited. > If we insist on more, it can be provided. Some of the present > ones will attempt to figure out which fraction corresponds > to a decimal representation of a number. > Most don't, and few care to ask for more, let alone pay for it. As I noted, outside of a few areas rational representation no longer exists. > When teaching I was repeatedly confronted by angry parents whose > children could not manipulate what I will call fractions (as opposed to > decimal fractions). They unanimously put forward the existence of > calculators to do the calculations, and calculators use decimals. Wall > Street now uses decimals. Banks no longer give 5 1/4%, but 5.25% I have seen Federal Reserve rates given in quarters. But > with the requirement of an APR, and with rates being > compounded at least monthly, if not daily, one almost > has to use rounded decimals. > One of the benefits of technology. Or is it just the fact that because it can be done it is done? 5% compounded daily is danged close to 5 1/4% compounded quarterly --- about 0.2% of principal. > Outside of a few trades like construction, where the English measuring > system still rules, fractions are disappearing from our society. We still use ounces and inches. There is also the use > of minutes and seconds, which corresponds to the ancient > base 60 notation. But I have seen few cookbooks which > point out that 1/3 of an ounce (liquid) is two teaspoons. > But we rarely do calculations on them. > And people do not understand the tragedy of this. As I have related int > he past, I have seen errors made because of a reliance on rote button > pushing caused by an undeserved faith in calculators. Adults do not > realize that 20% = 2/10, so they cannot calculate tips. They think that > a .300 wrench is huge, not being able to recognize it is 3/10. And on > and on and on. > Too many parents already teach their kids that math is hard. And now > htey put the calculator up as a method for making math easy. And if it > cannot be done on a calculator then it is too hard. This view comes from the emphasis on memorization and > computation the old-fashioned way. > No. This view comes from a history of not using math and parents that never took math classes in their schooling. 40% of the adults in my state did not graduate high school, and probably never took even an algebra I class. My mother dropped out (from anther state) at 14, which was routine. Only the 2 youngest of her 10 siblings graduated HS. It worked well for decades --- get out of school as early as 14, get a job in a textile mill or a factory, and earn enough to buy a house, 2 cars, and a big screen tv. They did not have to understand credit cards, income taxes, investments, etc. But the world changed, and they didn;t, so here we are. Larry > This goes beyond mere arithmetic. Graphing calculators are hurting > students' understanding. It takes very little to graph a line, with > understanding. I am not sure what you mean. It is easy with a ruler and > two points on the line, but I do not do a good job freehand. But still students push buttons, and have an undeserved > faith in the calculator. This is correct, but will the average student be able to > do any better? Calculators are super-fast sub-imbeciles, > and will do exactly what they have been told, no matter > how stupid it is. The tiny screen limits what can be displayed, > and important behavior beyond the display go unrevealed because students > think that what was displayed was *the* answer because they do not have > hte experience from manually graphing to know otherwise. How many points to graph? Also, while I do some manual > graphing, I prefer to put it on the computer, because I > do not do a good job. Understanding how is not adequate > without sufficient drawing skills. > i see students in other subjects that lose understanding because of > calculators. Finance majors do not understand the effects of changes in > period on interest because all the do is push buttons. Chemistry > students do not understand the gas laws because they program formulas > into a calculator and push buttons based on which variables are provided > in the question. > You put the rote calculations down, pushing instead for theory. We have seen what learning rote calculations does. We > have not seen, at the lower levels, what learning concepts, > not theory, can do, nor the advantages of learning theory. > Students who learned Euclid geometry do not seem to do any > worse than those learning geometry by calculation. > But most of us need the chance to explore and build relationships that > doing those calculations provides. Does doing the calculations achieve this? Or is it knowing > what things mean, and trying them out? Algebraic notation, > which is trivial, is what is needed. Yes, in the first grade doing rote > additon may sem barren, but it isn;t It develops skills, attitudes, and > expectations critical for success in many, many subjects in the future. But producing the addition tables by using successor, > and the multiplication tables by addition, will do a > better job of this. One cannot know that one can use something unless one knows > of its existence and its basic concepts. > Not true. > Many , many people, for example, use a pc without the slightest > understanding of how it works. In the extreme, they know to click on > this and their e-mail is displayed, and they are happy with this. They know the computer exists, and they know the concept > of email. > A scientist who understands the mathematical concepts needed > for his part of science can formulate his problems in such a > way that mathematicians not knowing his field of science can > come up with an answer, if it is known how to do so, or if one > can be deduced. Knowing a few procedures does not achieve > this result, and may achieve badly incorrect results. > Often the math concepts exceed the ability of the scientist,a nd rightly so. > For example, a professor friend did her dissertation on a graphing > technique that mapped amino acids in a large protein. The biologist > who wanted the info had a theory, but the need for PhD level math was > too much, so they formed a partnership. He provided the data, she > manipulated it. The biologist knew the concepts and could translate them into > mathematical terminology, so the mathematician could use the > power of mathematics. Alas, these days the emphasis is on > combining the two, and the resulting biomathematician will not > have either the understanding or the ability. > And they do have ideas about the properties of number, they just don;t > have the official names. In fact, the way I have taught math teaches > group and field theory, without using all of the formal names. > They know additive and multiplicative inverses, identities, closure. > They no symmetry, distance, and maybe even isomorphisms. They just do;t > know the vocabulary. > They also think that there is a great difference between > using Arabic numerals and Roman numerals. There is no > such difference, except some need to memorize. > The differences are significant. Roman numerals have no additive inverse > or identity, no multiplicative inverse, no placeholder. These are numerals, not numbers. Arabic numerals have no > inverses, etc. It is the numbers which do, and their > inverses do not depend on the representation. The > have the traces of that in minutes and seconds. > There is no zero in Roman numerals, a significant difference. There are > no negative roman numerals,nor fractions. Are there negative Arabic numerals? The use of negative numbers > was later. Zero as a digit was older, and used by the Sumerians > for their base 60 arithmetic more than 4000 years ago. The Egyptians had fractions, as did the Greeks and Romans. > The notation is not the concepts. > Roman numerals do not form a group. > They are not isomorphic with arabic numerals. It is only by using strings of Arabic numerals to > form representations of numbers, and the use of the > minus sign, that one can get the Arabic numerals to > form a group. The same could be done with the Roman > or Greek numerals, by adding bars for thousand times. > It should help > in understanding if students produce the addition and > multiplication tables to more than one base from first > ordinal principles, but memorizing them, no. > Yes, memorization of base 7 is worthless, and for all but computer nerds > any base except 10 is not needed. But is the memorization of the table needed? At most, it > is the ability to use the table. The Chisenbop method of > multiplication, which has been touted, only has products > by 1, 2, 5, and 10 learned; it uses the distributive law > for the rest. > Yes, the memorizations is vital. People cannot carry around a paper copy > if the table, so they carry a calculator. Then they rely on the > calculator for this operation, and eventually all operations. There is too much emphasis on memorization. > Why do the work when the calculator can do it? And the knee-jerk jump to > use the calculator eliminates the possibility of actually exploring the > situation. One can explore the situation by putting other entries into > the calculator, or by programming the computer to investigate > far more situations than can be done by hand. > Again, yes learning the tables is rote, drudge work, and maybe byt he > time you turn 60 you can start relying on machines to do the work. > But good habits start young, and bad habits start younger. In my state > calculators can be used as early as the 6th grade, and parents often let > their kids use them for homework even earlier. > And people wonder why kids cannot understand that 6 - 3 is really 6 + > (-)3 .The calculator uses the first expression., and that is all kids see. The Sumerians, Babylonians, Egyptians, Greeks, Romans, > and many more only used the first expression. They > did not know about negative numbers, and this applied > to the Arabs who took the Hindu numerals west. Do elementary school students learn the second? > No, it is needed to know that the base of the representation > is immaterial. Also, producing the tables from first principles > makes them meaningful, and not something to remember. It even > enables one to get by with forgetting some of it. > Bases are no more than a teaching tool for exponents and modulus. The > properties of the different bases are identical, and beyond showing they > are the sam as the decimal system bases are a curiosity for most. > Converting from decimal to base 8, for ex., is rote calculation at its > worst. > That said, an understanding of bases and modulus can be useful, in > particular as I noted in division. You are using modulus in a non-mathematical sense here. > No It turns them into programmers, not mathematicians. What does knowing how to do arithmetic do? It turns > them into the equivalent of the machine doing the > result of the programming. > But that requires an understanding of numbers, while the use of > calculators does not. No amount of facility at arithmetic yields an understanding > of numbers. > I disagree, and we will have to agree to disagree. > I suspect you are approaching this from a far higher theoretical level > than most people reach. I want first graders to reach this level, and I believe > most can do it with ease if the ordinal approach is the > first used. It is SIMPLE. But trying to teach it to > high school and college students is very difficult; they > know the numbers, and are unwilling to learn the basics > which they do not know at all. > Most first graders are incapable of doing what you want. Getting them to > even learn the basics of the integers is a full time job. But the basics of the integers from the Peano Postulates and > the base 1 notation are easy. It is using base 10 from the > beginning which makes it harder. Do YOU know the basics of the integers? Knowing them does not > require being able to count above 3, although I may be somewhat > wrong on just how high. I am not even sure if Landau's book > even gets to 2, except for the numbering of statements, etc. > Yes, I do. > You are oversimplifying and isolating the concepts. I am pointing out that the concepts are simple. > Teaching math to older students is difficult not because they think they > know it all, but because by the time they reach that age society has > taught them that math is irrelevant. How about teachers who are going to teach math? > I saw it in my classes to the point that students changed their majors, > even elementary ed majors. They could not do the work even inthe math > for middle school courses. > Getting > non-computational concepts to them is almost a lost cause; > many never get it. > Because they have never been exposed to them, usually because technology > has taken the lead. > And how about the 80% of prospective > high school teachers of math who could not set up a problem > using calculus, in a course which had the full calculus > prerequisite, on a take-home final? > I need more info on this. This was in a probability course. The problems were quite > similar to those done in class. > For ex., my college strongly suggested that prospective teachers take > the certification exams early and often even before the preparation > courses had been taught. > Certification standards are also changin; now most states require at > least a BA in math to teach HS math, and no one can get that degree and > not set up a calculus equation. Unfortunately, this is false. They can calculate derivatives > and anti-derivatives, but the rest is forgotten. > Heck, many states and national > certification now even require formal proofs to teach HS math Do they require them to pass an examination? Having taken > courses which taught this is not sufficient. > The math professors > who taught them were not surprised; they are quite aware > that the bulk of calculus students can only memorize formulas > and their use. They are not even at the level of programmers; > they are at the level of the computer hardware. > That is the fault of the professors, not the students. My professors > would not pass a student wh could not explain what they were doing, and > absolutely refused to allow the use of technology. If the professors did not do this, the enrollment in calculus > courses would drop drastically. Engineers and physicists do > not care, as far as their courses are concerned, whether there > is understanding, and would teach the students themselves. Using technology is another matter. How do you expect students > to get the square root of 1.37 on an exam? Technology was used > for such even BC (before computers); slide rules were used. And > slide rules were used for multiplying back then. > Larry > === Subject: Re: K-12 Calculator Woes ................ > Knowing how to do arithmetic is useful, but not > essential. Understanding the numbers, and I do not > mean strings of numerals, is essential, and most of > our high school teachers of mathematics do not have > any of that. > Using calculators removes students from the numbers, hindering > understanding. > No, it does some removing students from operators > with sequences of numerals. The understanding does > not at all come from familiarity with arithmetic, > but in understanding numbers as such. > And calculators remove the need to understand numbers, replacing that > understanding with an understanding of programming calculators. > Understanding numbers is NOT understanding strings of > decimal digits. There are two main concepts for the > integers, and neither of them has anything to do with > the decimal representation. > The decimal representation is only ONE way of representing > numbers; it is sometimes not even useful. > For 99% of he population it is the only way of representing and > manipulating numbers. Even rational fractions disappear from their > lexicon for most, unless they user a tool like a tape measure. Heck, > even fractions have virtually disappeared from he stock market. > There are other means as well. Those in the sciences, and > in many other fields as well, misuse mathematics because > they have learned procedures which require assumptions to > be met to be valid. >You continue to miss the point. >Yes, there are other methods, like base 16 for carpentry using >caricatures of tools instead of letters and numerals because studs are >16 inches on center. If one understands the numbers, integer, fractional, real, and if need be complex (try handling AC circuits without it), the representation becomes of little importance. Being able to make limited use of a particular representation does NOT convey understanding. No matter how well one does base 10 arithmetic, this conveys no more than having the mechanical processes in ones memory banks. There is not even understanding of the processes. >But for those out there in the real world other methods do not exist, >either because they are unaware of them, because their technology cannot >handle them, or they just plain flat out refuse to acknowledge their >existence. If they are unaware of them, how can they know if they can make use of them? If they refuse to acknowledge their existence, can they be said to be educated about the numbers? >Why us a base 16 measuring system when the base 10 is perceived to be >better, the technology is designed around that system and they already >know it? Computer technology is NOT designed about base 10, and will not be in the future. It is really base 2, but 16 is used as a convenient version so that expressions will not be too long. >Does any other system work better. Absolutely no!. Talk a bout wasting >time and effort! See the above. There are other places where these come in. > They have NOT. The string 6.43 means 6 plus 43/100. If they > do not understand the decimal fractions are fractions, they do > not understand decimal fractions. > I said the rational representation of fractions. > I agree that not enough is done with this, and that > computers have a lot to do with the problem. It is > easy to get computers to run in base 2 arithmetic, > including for real numbers, and even the important > fixed-point arithmetic is difficult on them. The > representation of fractions is, for a machine, much > harder than floats or decimals, and is more complicated > to work with. > However, the teaching of fractions leaves even more > to be desired. In can be made both rigorous and > more simple. Of course, anything is simpler if one > has algebraic notation, by which I mean that a > variable is a symbolic expression which can stand > for anything. So we have, for h not 0, > a/b = ah/bh, > and if the idea of fractions is presented with a > modicum of intelligence, it is obvious that > a/b + c/b = (a+c)/b. >I don;t know about your school district, but that is part of my >districts middle school curriculum. Do they use algebraic notation? Do they still ask students to use the least common denominator? >You suggest that 6 yr olds can handle this. I disagree, and most other s >do, too, because most 6 yr old have not reached the mental stage to >understand representation. They are still in a concrete world. I have never suggested that 6 year olds have the understanding of integers needed to start on fractions. I do not know how fast one can do the work, nor do I have any objection to them learning arithmetic operations to base 10 before doing much, or even starting, with fractions. Children are capable of understanding abstract ideas, NOT as abstractions. It is this confusion that too many are making; an abstract idea may have come about as the result of a process of abstraction, but it is more than that, and easier to understand if taught directly. >I also agree with you that too many early ed teachers lack the math >understanding to teach this. But that is slowly changing as a ndew crop >of teachers enters the schools. I, for ex, was he first math certified >teacher in my middle school, the others were gen ed. 4 years later all 4 >8th grade math teachers are math certified (i'm gone). > Because of calculators people do not use that form, and they cannot > manipulate them, and often cannot understand them. > My concern is that they understand them, and hence > can properly use them. >My experience is they have no idea how hey work, they are magic black >boxes. Even worse, they have no interest in understanding how they work, >even to the point that they refuse to even try. Starting in the 4th grade. Whether they know exactly how the black box works is not a problem; they need to know how the numbers work. Teach concepts, and these problems might well not even arise. >Why bother to understand how a tv works? Push certain buttons and good >things happen. Or a pc, microwave, elevator, or cell pone. >Most don;t care until they break, then they go to an expert to fix it, >or even worse, throw the broken one away and get a new one. This is not the problem. They need to understand the concepts involved in viewing a TV. These are only optical. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) ................ Knowing how to do arithmetic is useful, but not > essential. Understanding the numbers, and I do not > mean strings of numerals, is essential, and most of > our high school teachers of mathematics do not have > any of that. > Using calculators removes students from the numbers, hindering > understanding. No, it does some removing students from operators > with sequences of numerals. The understanding does > not at all come from familiarity with arithmetic, > but in understanding numbers as such. > And calculators remove the need to understand numbers, replacing that > understanding with an understanding of programming calculators. Understanding numbers is NOT understanding strings of > decimal digits. There are two main concepts for the > integers, and neither of them has anything to do with > the decimal representation. The decimal representation is only ONE way of representing > numbers; it is sometimes not even useful. > For 99% of he population it is the only way of representing and > manipulating numbers. Even rational fractions disappear from their > lexicon for most, unless they user a tool like a tape measure. Heck, > even fractions have virtually disappeared from he stock market. There are other means as well. Those in the sciences, and > in many other fields as well, misuse mathematics because > they have learned procedures which require assumptions to > be met to be valid. You continue to miss the point. I think the problem is you two are talking about two different points. IMO the purpose of a math class is not to teach maths but to teach a mode of knowing---of course, the only way available to do that is to teach some mathematics, so the teaching of maths in a good math class is unavoidable. But as soon as we lose sight of the fact that the real purpose is not to have students know facts about, say, numbers but to know them in a specific way, chaos (in various manifestations) follows. It is my conclusion after having participated in way too many discussions about math education (at the college level but, really, mutatis mutandi, the issues are exactly the same as in any other level) that essentially all disagreements are due to the opposing parties having a different opinion on this. Moreover, in the enormous majority of cases none of the parties recognize that the matter of contention is not material (*what* subjects to teach?, for example) but epistemiological---and this results in countless hours/emails of argumentation for and against the teaching of various subjects and other trivia, discussion which will never ever help in getting close to an agreement for it is a discussion on something rather irrelevant to the disagreement. This is entirely similar to the debates between the right and the left when it turns to the minutiae of the management and implementation of policies, while leaving aside the ideological and programmatic side of things---side which, nowadays, has really bad press, for we are, as we all know, living in post-ideological times... -- m === Subject: Re: K-12 Calculator Woes .................... <> Knowing how to do arithmetic is useful, but not <> essential. =A0Understanding the numbers, and I do not <> mean strings of numerals, is essential, and most of <> our high school teachers of mathematics do not have <> any of that. <> Using calculators removes students from the numbers, hindering <> understanding. <> No, it does some removing students from operators <> with sequences of numerals. =A0The understanding does <> not at all come from familiarity with arithmetic, <> but in understanding numbers as such. <> And calculators remove the need to understand numbers, replacing= > that <> understanding with an understanding of programming calculators. <> Understanding numbers is NOT understanding strings of <> decimal digits. =A0There are two main concepts for the <> integers, and neither of them has anything to do with <> the decimal representation. <> The decimal representation is only ONE way of representing <> numbers; it is sometimes not even useful. =A0 <> For 99% of he population it is the only way of representing and <> manipulating numbers. Even rational fractions disappear from their <> lexicon for most, unless they user a tool like a tape measure. Hec= >k, <> even fractions have virtually disappeared from he stock market. <> There are other means as well. =A0Those in the sciences, and <> in many other fields as well, misuse mathematics because <> they have learned procedures which require assumptions to <> be met to be valid. =A0 > You continue to miss the point. >I think the problem is you two are talking about two >different points. >IMO the purpose of a math class is not to teach maths >but to teach a mode of knowing---of course, the only >way available to do that is to teach some mathematics, >so the teaching of maths in a good math class is unavoidable. Knowing WHAT? >But as soon as we lose sight of the fact that the real purpose >is not to have students know facts about, say, numbers but to >know them in a specific way, chaos (in various manifestations) >follows. It is NOT important to know facts, other than a few, but to UNDERSTAND. The present methods of teaching teach lots of facts, but little or even NO understanding. As of this time, the students coming out of a calculus class may know many facts and methods, but few of them will have an understanding of derivative or integral. Concepts are not taught by teaching the words, but by getting the student to internalize the ideas. >It is my conclusion after having participated in way too >many discussions about math education (at the college level >but, really, mutatis mutandi, the issues are exactly the same >as in any other level) that essentially all disagreements >are due to the opposing parties having a different opinion >on this. Moreover, in the enormous majority of cases none >of the parties recognize that the matter of contention is >not material (*what* subjects to teach?, for example) but >epistemiological---and this results in countless hours/emails >of argumentation for and against the teaching of various >subjects and other trivia, discussion which will never ever >help in getting close to an agreement for it is a discussion on >something rather irrelevant to the disagreement. No, you do not get it. I would require much of a good course on real variables before calculus. Solving problems is not the goal, except for adepts; knowing the concepts well enough to set up the problem and communicate with the specialist is primary. Only then does one become a specialist. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: P=NP Proof Published at CERN Martin Musatov a .8ecrit : > An informal and highly experimental, unorthadox > proof P=NP has been > published on CERN preprints. > > http://cdsweb.cern.ch/record/1164206/files/s1-ln575821 > 0-9223534-1939656818Hwf-1468147288IdV-1521282711575821 0PDF_HI0001.pdf It is mine, and no it is not published anywhere > else. My purpose in > posting it here is for feedback and suggestions > on > how to strengthen > it. I would specifically, as was my intention with > this > experiment, like > feedback from anyone interested in the > methodology > I used and > suggestion as to how I might go about pursuing a > more broadly accepted > peer-reviewed published proof building on this > basic result. > Dont worry : if you have really proved P=NP, any > working program solving > any NP-complete problem in polynomial time will be > enough to bring you > fame, the Clay prize money, and perhaps even > chicks... Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. > Only a fool delights in mockery and speaks without control of his words. The words I speak are measured and logical. I do not delight in disproof but revel in truth. A fool scorns but spares the details and fails to address specifics. Vagueness is the last refuge for ignorance and complexity the last stronghold belonging to the leviathan.Do not be sad at the reference to CERN. The link is good and the work is solid. If anything, rejoice! > Fool ! its just another crank , the reference to CERN only > makes its sad.I do not know who JSH is so I will not answer you on this charge. L:23:He who guards his mouth and his tongue keeps himself from calamity. Proverbs, Chapter 21, Verse 23. I do not need luck. The universe itself speaks in my defense.__Martin Musatov P.s. I do not make a penny on my work$. These words are free as they should be. Mathematics is the greatest thing that ever happened to me. I am so excited to learn and share and too busy to address my critics who scorn me but fail to provide details or explain anything they say. you wouldnt recognize a real crank , if he bites your > nose ! the P = NP proof is bogus !! i cant believe mentioning CERN is enough to trick you > ! you still amaze me , but in a bad way ! cmon , JSH does better than that ! i hope no money was spent on that piece of crap ... tommy1729 === Subject: Re: P=NP Proof Published at CERN 8XPM9-7F9HD-4JJQP-TP64Y-RPFFV 762HW-QD98X-TQVXJ-8RKRQ-RJC9V I Just Proved [P=NP] and I get to announce it on Usenet. Source: http://coding.derkeiler.com/Archive/General/comp.theory/200904/msg00122.html http://ar.wikipedia.org/wiki/FB'4_'DE3*./E:9DJ_'D('4'_2 'D1,'! 'DE4'1C) AJ 'D*5HJ* D*/J/ E3*B(D 41H7 BHB 'DF41 AJ E4'1J9 HJCJEJ/J' (JF*GJ 'D*5HJ* AJ 3 E'JH 2009). 5H* 'DF! 7D('* 'D5HD 9DI 'DEF 'D/1'3J) DHJCJE'FJ' 2009 EA*H) 'DF 3,D 'DF [#:DB] [3'9/F' AJ 'D*1,E)!] F/9HC DDE3'GE) AJ #3(H9 'D*'1J. 'D93C1J HGH #/ 'D#3'(J9 'DE*9//) EF #3'(J9 'DHJCJ. [#:DB] FB'4 'DE3*./E:9DJ 'D('4' 2 EF HJCJ(J/J' 'DEH3H9) 'D1) *H,/ D/JC 13'&D ,/J/) (.1 *:JJ1). Making use of a new type of modeltheoretic tool the Boolean Sieve we have been able to construct a Ptime algorithm for SAT, thus providing a resolution to one of the most famous, longstanding open problems of Theoretical Computer Science. A detailed, but accessible and informal, general overview of the Boolean Sieve method (more information can be found here by carrying out a Google groups search under Boolean Sieve and Mathematician's Algorithm). However, a brief description will be provided below of the method, some applications outside the specific context of SAT, as well as an overview of how it was applied to SAT. Opportunity providing, an abstract or possibly even an online copy of the submitted paper (just accepted for publication) will be made available at the above Web site. What is a Boolean Sieve? Basically, it is a construct that is generated from a set of models, for an axiomfree theory (free theory), that are defined to filter out the possible logical relations between a set of statements which could be rendered in that theory. A possible application may be to seek out significant axiomatizations that may be applied to the set of operations and predicates in the underlying free theory. The term filter is more than appropriate given the nature of the formal machinery behind the method. For instance, consider Group Theory. An interesting (but not well known) fact is that groups can be defined by their inverse operation I Just Proved [P=NP] and I get to announce it on Usenet. I Just Proved [P=NP] and I get to announce it on Usenet.1 (division), just as well by multiplication. The underlying free theory is an algebraic sort with the following set of operations: () |> 1 (identity) (a, b) |> a/b (quotient) So, it then becomes natural to ask: what are the logical relations between the possible statements that could be made over the underlying free theory. Such a situation is precisely the kind of circumstance where one would use the Boolean Sieve method. What one does is write down a bunch of statements (ideally, including a set of statements that we already know from prior considerations would completely characterize a group), and then select a bunch of models for the free theory (which in the case at hand may or may not actually be groups). Each model should have the property that each statement has a truth value whose evaluation in that model can be done efficiently. The result is a set of raw data from which a profile can be assembled. The method of integrating all the basic facts is the Boolean Sieve, itself. The result of applying the Sieve is an efficient characterization, as a set of Horn clauses, of the Boolean lattice off the significant relations and possible axiomatizations, e.g., (a/c)/(b/c) = a/b; a/a = 1; a/1 = a or for Abelien groups: a(bc) = c(ba); a(ab) = b; 11 = 1. More generally, a Boolean Sieve will allow us to filter out the possible relations between a set of statements. The Sieve is called Complete for that set, if all possible relations are constructed by the Sieve. What we've actually done is resolve a generalization of SAT (i.e., determine the validity of a Horn clause involving Boolean formulas over Nvariables) by defining a process (that is N^3 in complexity) that generates a complete Boolean Sieve that is N^3 in size. Why N^3? Well, this is where it gets interesting: the method for generating the complete Boolean Sieve is essentially a disguised version of the Earley parsing algorithm for contextfree grammars! The significance and nature of this link remains a total mystery to us. Currently, we are investigating extensions of the Boolean Sieve which will provide a basis for modeltheoretic theorem proving methods or Semantic Theorem Proving. As any expert mathematician will be able to relate, such an appropach has a far more direct bearing on the way mathematicians actually approach problems. They will take a stock set of examples, run a set of possible statements through the examples (oftentimes subconsciously) and magically arrive at a set of conjectures. We conjecture that the latent method behind this process is none other than the Boolean Sieve, itself. We even speculate that mathematical intuition, itself, may be nothing more than the by product of this subconscious process. Thus, for instance, one could develop a more honed intuition by having a larger stock of ready made examples under the belt, so to say. Needless to say, these developments will go far beyond the specifics of the P = NP problem, as most anyone would have been able to I Just Proved [P=NP] and I get to announce it on Usenet. I Just Proved [P=NP] and I get to announce it on Usenet.2 > On 9 May, 09:18, Martin Musatov > An informal and highly experimental, unorthadox > proof Does that mean bogus? P=NP has been > published on CERN preprints. 8XPM9-7F9HD-4JJQP-TP64Y-RPFFV 762HW-QD98X-TQVXJ-8RKRQ-RJC9V I Just Proved [P=NP] and I get to announce it on Usenet. Source: http://coding.derkeiler.com/Archive/General/comp.theory/200904/msg00122.html http://ar.wikipedia.org/wiki/FB'4_'DE3*./E:9DJ_'D('4'_2 'D1,'! 'DE4'1C) AJ 'D*5HJ* D*/J/ E3*B(D 41H7 BHB 'DF41 AJ E4'1J9 HJCJEJ/J' (JF*GJ 'D*5HJ* AJ 3 E'JH 2009). 5H* 'DF! 7D('* 'D5HD 9DI 'DEF 'D/1'3J) DHJCJE'FJ' 2009 EA*H) 'DF 3,D 'DF [#:DB] [3'9/F' AJ 'D*1,E)!] F/9HC DDE3'GE) AJ #3(H9 'D*'1J. 'D93C1J HGH #/ 'D#3'(J9 'DE*9//) EF #3'(J9 'DHJCJ. [#:DB] FB'4 'DE3*./E:9DJ 'D('4' 2 EF HJCJ(J/J' 'DEH3H9) 'D1) *H,/ D/JC 13'&D ,/J/) (.1 *:JJ1). Making use of a new type of modeltheoretic tool the Boolean Sieve we have been able to construct a Ptime algorithm for SAT, thus providing a resolution to one of the most famous, longstanding open problems of Theoretical Computer Science. A detailed, but accessible and informal, general overview of the Boolean Sieve method (more information can be found here by carrying out a Google groups search under Boolean Sieve and Mathematician's Algorithm). However, a brief description will be provided below of the method, some applications outside the specific context of SAT, as well as an overview of how it was applied to SAT. Opportunity providing, an abstract or possibly even an online copy of the submitted paper (just accepted for publication) will be made available at the above Web site. What is a Boolean Sieve? Basically, it is a construct that is generated from a set of models, for an axiomfree theory (free theory), that are defined to filter out the possible logical relations between a set of statements which could be rendered in that theory. A possible application may be to seek out significant axiomatizations that may be applied to the set of operations and predicates in the underlying free theory. The term filter is more than appropriate given the nature of the formal machinery behind the method. For instance, consider Group Theory. An interesting (but not well known) fact is that groups can be defined by their inverse operation I Just Proved [P=NP] and I get to announce it on Usenet. I Just Proved [P=NP] and I get to announce it on Usenet.1 (division), just as well by multiplication. The underlying free theory is an algebraic sort with the following set of operations: () |> 1 (identity) (a, b) |> a/b (quotient) So, it then becomes natural to ask: what are the logical relations between the possible statements that could be made over the underlying free theory. Such a situation is precisely the kind of circumstance where one would use the Boolean Sieve method. What one does is write down a bunch of statements (ideally, including a set of statements that we already know from prior considerations would completely characterize a group), and then select a bunch of models for the free theory (which in the case at hand may or may not actually be groups). Each model should have the property that each statement has a truth value whose evaluation in that model can be done efficiently. The result is a set of raw data from which a profile can be assembled. The method of integrating all the basic facts is the Boolean Sieve, itself. The result of applying the Sieve is an efficient characterization, as a set of Horn clauses, of the Boolean lattice off the significant relations and possible axiomatizations, e.g., (a/c)/(b/c) = a/b; a/a = 1; a/1 = a or for Abelien groups: a(bc) = c(ba); a(ab) = b; 11 = 1. More generally, a Boolean Sieve will allow us to filter out the possible relations between a set of statements. The Sieve is called Complete for that set, if all possible relations are constructed by the Sieve. What we've actually done is resolve a generalization of SAT (i.e., determine the validity of a Horn clause involving Boolean formulas over Nvariables) by defining a process (that is N^3 in complexity) that generates a complete Boolean Sieve that is N^3 in size. Why N^3? Well, this is where it gets interesting: the method for generating the complete Boolean Sieve is essentially a disguised version of the Earley parsing algorithm for contextfree grammars! The significance and nature of this link remains a total mystery to us. Currently, we are investigating extensions of the Boolean Sieve which will provide a basis for modeltheoretic theorem proving methods or Semantic Theorem Proving. As any expert mathematician will be able to relate, such an appropach has a far more direct bearing on the way mathematicians actually approach problems. They will take a stock set of examples, run a set of possible statements through the examples (oftentimes subconsciously) and magically arrive at a set of conjectures. We conjecture that the latent method behind this process is none other than the Boolean Sieve, itself. We even speculate that mathematical intuition, itself, may be nothing more than the by product of this subconscious process. Thus, for instance, one could develop a more honed intuition by having a larger stock of ready made examples under the belt, so to say. Needless to say, these developments will go far beyond the specifics of the P = NP problem, as most anyone would have been able to I Just Proved [P=NP] and I get to announce it on Usenet. I Just Proved [P=NP] and I get to announce it on Usenet.2 === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) I would like feedback on the P==NP problem. I--MMM > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. -- m === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. -- m You can figure it out, I have faith in you. But in case you lack faith in yourself the feedback I am seeking on is [P==NP].on. -- m === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > An informal and highly experimental, unorthodox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. that did not get mangled) even remotely similar to anything related to > computational complexity theory > on. ] on.<[ -- m a singer. ±±Frank Sinatra === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Vagueness is the last refuge for ignorance. Complexity is the last refuge for evil. > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. *What specifically is unintelligible? Vagueness is the last refuge for ignorance. Complexity is the last refuge for evil.--Martin Musatov -- m === Subject: Re: P=NP Proof Published at CERN posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Vagueness is the last refuge for ignorance. Complexity is the last > refuge for evil. An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. >http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. > *What specifically is unintelligible? It does not even qualify as a text, let alone as a coherent exposition of an heuristic which may or may not resolve a mathematical problem. I simply cannot believe you are serious, for even a minimally trained Markov chain will do a better job both at coming up with English prose and at following minimal usenet conventions in composing posts: even BURT makes more sense and is more articulate than you are, and you are less intruiguing than him too. I trust you will not be particularly disrupted in your pursuits if I start ignoring you from now on, so I will. -- m === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Sometimes what you read is just as important as what you read into it. --Martin Musatov > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. -- m === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) On 10 May, 19:29, Martin Musatov top- replied: > Sometimes what you read is just as important as what you read into > it. --Martin Musatov So what is there to read, or read into in gibberish like - Show quoted text - > Expansion of a sum (Taylor Series) [4];. > 1+.. ..=1+ > .... > 1! > + > .. ..-1 ..22! > +. > Followed by the Fourier Series [5]:. > .. .. =..0+ ....cos > ...... > .. > +....sin > ...... > .. > 8 > ..=1 ? === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > Discussions - sci.math.symbolic | Google Groups > The polynomials in y, P(n,y) := #i^n/n * B(n, -#i*y) + #i/2 * y^(n-1) > then have real ... [sage-devel][P=NP] > An informal and highly experimental, unorthodox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hw f -1468147288IdV-15212827115758210PDF_HI0001.pdf It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > ****Denis: I understand the effort required to keep a nice garden, so > I apologize if I trampled your shrubs. Re:http://www.ietf.org/html.charters/ecrit-charter.html, > though I hope you're right re: neat results, Millenium Prize money, Millennium. > and the ladies! (though my heart is really with only one) > ****victor_meldrew_...@yahoo.co.uk: I like a fool misspelled > orthodox. While you share the same first name with my father I can > only pray the reason the 666 is there because 2/3 didn't fit. > Re: Does that mean it's bogus? ***You tell me: What it is is an unintelligible mish-mash that no self-respecting crank would have released to the world. Did you even bother to look at your own pdf? > NOTE: The Google Docs parsing began generating content vertically as > it ran the equations I had prepared in a Microsoft Word file, Real Mathematicians do not use Macro Turd. > So indeed my proof What ing proof? 1+.. ..=1+ > .... > 1! > + > .. ..-1 ..22! > +. > Followed by the Fourier Series [5]:. > .. .. =..0+ ....cos > ...... > .. > +....sin > ...... > .. > 8 > ..=1 And you want us to bow down to your genius becuase you write crap like this? === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) ****Denis: I understand the effort required to keep a nice garden, so > I apologize if I trampled your shrubs. Re:http://www.ietf.org/html.charters/ecrit-charter.html, > though I hope you're right re: neat results, Millenium Prize money, Millennium. and the ladies! (though my heart is really with only one) > ****victor_meldrew_...@yahoo.co.uk: I like a fool misspelled > orthodox. While you share the same first name with my father I can > only pray the reason the 666 is there because 2/3 didn't fit. > Re: Does that mean it's bogus? ***You tell me: What it is is an unintelligible mish-mash that no self-respecting > crank would have released to the world. Did you even bother > to look at your own pdf? NOTE: The Google Docs parsing began generating content vertically as > it ran the equations I had prepared in a Microsoft Word file, Real Mathematicians do not use Macro Turd. So indeed my proof What ing proof? Expansion of a sum (Taylor Series) [4];. > 1+.. ..=1+ > .... > 1! > + > .. ..-1 ..22! > +. > Followed by the Fourier Series [5]:. > .. .. =..0+ ....cos > ...... > .. > +....sin > ...... > .. > 8 > ..=1 And you want us to bow down to your genius becuase you write > crap like this? Might you be so kind as to share the abstract . I do not recall mentioning bowing down. May I request a reference for this statement. Signed, Martin Musatov === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) ****Denis: I understand the effort required to keep a nice garden, so > I apologize if I trampled your shrubs. Re:http://www.ietf.org/html.charters/ecrit-charter.html, > though I hope you're right re: neat results, Millenium Prize money, Millennium. and the ladies! (though my heart is really with only one) > ****victor meldrew ...@yahoo.co.uk: I like a fool misspelled > orthodox. While you share the same first name with my father I can > only pray the reason the 666 is there because 2/3 didn't fit. > Re: Does that mean it's bogus? ***You tell me: Y+ur +pinti+n mish-mash that this self-respecting > crank released to the world. Yes, I did: > Look at owner pdf: All systems go: NOTE: The Google Docs parsing began generating content vertically as > it ran the equations I had prepared in a Microsoft Word file: Real mathematicians are professional and polite. So indeed my proof: This proof: Expansion of a sum (Taylor Series) [4];. > 1+.. ..=1+ > .... > 1! > + > .. ..-1 ..22! > +. > Followed by the Fourier Series [5]:. > .. .. =..0+ ....cos > ...... > .. > +....sin > ...... > .. > 8 > ..=1 === === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) * {{rhymes|?¢¡(r)m?l}} > {{en-adj}} > # Not [[formal]] or [[ceremonious]]; [[casual]]. > #: ''an '''informal''' get-together'' > # Not in [[accord]] with the [[usual]] [[regulation]]s; > [[unofficial]]. what's the point of this? === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I have apparently been reviewed again as he page parsed at CERN and > gave a new URL: > Here it is:http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... New URL, same old . === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) constructive work. I have apparently been reviewed again as he page parsed at CERN and > gave a new URL: > Here it is:http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... New URL, same old . === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) On 10 May, 19:26, Martin Musatov top- replied: > Please refrain from cussing. Please refrain from breathing. === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Also here are some additional related results: 1) Access to > Photograph:http://documents.cern.ch/cgi-bin/setlink?base=PHO&categ=photo-tsi c &id... > 2)Conversions Information: Portable Document Format:http:// > documents.cern.ch/archive/electronic/hep-lat/9612/9612008.pdf Wgat have these to do with your drivel? > Does that mean bogus?. No, you are welcome to try to disprove it. There is nothing there to disprove; it's not even wrong. === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) So we have proven given falseproof not even wrong=proof= > Also here are some additional related results: 1) Access to > Photograph:http://documents.cern.ch/cgi-bin/setlink?base=PHO&categ=photo-tsi c &id... > 2)Conversions Information: Portable Document Format:http:// > documents.cern.ch/archive/electronic/hep-lat/9612/9612008.pdf Wgat have these to do with your drivel? Does that mean bogus?. No, you are welcome to try to disprove it. There is nothing there to disprove; it's not even wrong. === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > So we have proven given falseproof not even wrong=proof= And you have top-replied with yet more gibberish. === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) What have these to do with your inability to spell the word *what*? Ask politely and constructively and I will answer. If not, get behind me and push. > Also here are some additional related results: 1) Access to > Photograph:http://documents.cern.ch/cgi-bin/setlink?base=PHO&categ=photo-tsi c &id... > 2)Conversions Information: Portable Document Format:http:// > documents.cern.ch/archive/electronic/hep-lat/9612/9612008.pdf Wgat have these to do with your drivel? Does that mean bogus?. No, you are welcome to try to disprove it. There is nothing there to disprove; it's not even wrong. === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > What have these to do with your inability to spell the word *what*? > Ask politely and constructively and I will answer. If not, get behind > me and push. the knife in? === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > My name is Martin Michael Musatov and I am an Independent Researcher in Los Angeles, California with academic and intellectual rights to a photo on your server. I am formally requesting in writing the Meta tags and accreditation site wide pertaining to this photograph and the body of work which surrounds it be updated per the list below: Photo & Credits: Light-Symmetry: Photograph by Michelle Musikantow, Jerusalem, Israel. Principal Light-Symmetry theory, formulated by Martin M. Musatov. Caption: (optional) This picture describes broad-lay of P=NP as Light-Symmetry. List of files to which this request applies: 1. Loose Image: http://documents.cern.ch/photo/photo-tsic/icon-dfbx-2009-001.gif 2. Record/proof of my prior submission: http://cdsweb.cern.ch/record/1164207/export/xm 3. CDS Page: http://documents.cern.ch/cgi-bin/setlink?base=PHO&categ=photo-tsic&id=dfbx-2 0 09-001 4. Seed for conversions information: http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hw f-1468147288IdV-15212827115758210PDF HI0001.pdf 5. 6. Conversions Information: http://documents.cern.ch/archive/electronic/hep-lat/9612/9612008.pdf I do thank you for your time and careful attention with this matter. Martin Musatov > It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > My name is Martin Michael Musatov and I am an Independent > Researcher Is Independent Researcher your euphemism for idiot? === Subject: Re: P=NP Proof Published at CERN > A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. I prefer to think of it as the middle 20 pages somehow got cut out, since the geometry had to be somehow related to computational complexity... -- Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) On May 9, 12:15pm, Mariano Su.87rez-Alvarez An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. -- m === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Understanding Godel is not God is equally important. Understanding logic is more important. On May 9, 12:15?pm, Mariano Su?rez-Alvarez > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. >http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. > I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. > -- m > If you want help you have to make a readable copy of the > proof available. > David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) === Subject: Re: P=NP Proof Published at CERN <090520090900584812%anniel@nym.alias.net.invalid> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > 1468147288IdV-15212827115758210PDF HI0001.pdf It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. The mathematics formulas in that PDF are unintelligible. Was that done re: The mathematics formulas in that PDF are intelligible to most when or CERNm when it was put on-line or after does it matter to us here and now as we read: please see: http://www.MeAmI.org/wiki/?NPComplete and http://meami.org/wiki//index.php?P%3DNP%20Problem and finally for those math equations: page 3. http://member.thinkfree.com/myoffice/show.se?f=a2262e3b4f62ab0338f0d41fde4ff b 82 === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > or CERNm when it was put on-line or after does it matter to us here So it was definitely not bungled by Martin Musatov? === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Yes. or CERNm when it was put on-line or after does it matter to us here So it was definitely not bungled by Martin Musatov? Yes. === Subject: Re: P=NP Proof Published at CERN <090520090900584812%anniel@nym.alias.net.invalid> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > 1468147288IdV-15212827115758210PDF HI0001.pdf It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. The mathematics formulas in that PDF are unintelligible. Was that done The mathematics formulas in that PDF are identical to as they were in parsing on p.3 of this document here. > http://member.thinkfree.com/myoffice/show.se?f=a2262e3b4f62ab0338f0d41fde4ff b 82 The whole expansion on page 3. m[dot]mm[at]vzw[dot]blackberry[dot]net.~~~~ === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) An informal and highly experimental, unorthodox proof P=NP has been > published on CERN preprints. >http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > 1468147288IdV-15212827115758210PDF HI0001.pdf It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. The mathematics formulas in that PDF are intelligent. Was that done The mathematics formulas in that PDF are identical to as they were in parsing on p.3 of this document here. > http://member.thinkfree.com/myoffice/show.se?f=a2262e3b4f62ab0338f0d41fde4ff b 82 The whole expansion on page 3. === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) On May 9, 12:15pm, Mariano Su.87rez-Alvarez An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least > that did not get mangled) even remotely similar to anything related to > computational complexity theory is not something you can get feedback > on. > It is actually even impossible to see *what* it is you want feedback > on. -- m familiar with the Internet...a huge+ re: --m: Facts in Proof. Evidence. Evaluation of Evidence, (that is very, very, thoughtful and patience of you to react with such kindness, care, insight, and attention to detail even when it is sometimes painfully obvious the secret missing logical component needed to definitively refute any proof: P=/=NP and counter it with shrewd humanitarian based logic of ages grounded as much in science and cold physical studies as it is in morality). *In polynomial time responses can be handled efficiently if the programmer considers possibilities before they occur. Good point, just because something you were prepared for occurs does not mean you are the cause.--Martin Musatov Critique my method to this statement as it satisfies an axiom to prove P==NP. *Critique my approach in Polynomial time to what we need to get P==NP published to claim: The Clay Mathematics Institute (CMI) of Cambridge, Massachusetts has named seven Millennium Prize Problems. The Scientific Advisory Board of CMI (SAB) selected these problems, focusing on important classic questions that have resisted solution over the years. The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each. The Directors of CMI, and no other persons or body, have the authority to authorize payment from this fund or to modify or interpret these stipulations. The Board of Directors of CMI makes all mathematical decisions for CMI, upon the recommendation of its SAB. The SAB of CMI will consider a proposed solution to a Millennium Prize Problem if it is a complete mathematical solution to one of the problems. (In the case that someone discovers a mathematical counterexample, rather than a proof, the question will be considered separately as described below.) A proposed solution to one of the Millennium Prize Problems may not be submitted directly to CMI for consideration. Before consideration, a proposed solution must be published in a refereed mathematics publication of worldwide repute (or such other form as the SAB shall determine qualifies), and it must also have general acceptance in the mathematics community two years after. Following this two-year waiting period, the SAB will decide whether a solution merits detailed consideration. In the affirmative case, the SAB will constitute a special advisory committee, which will include (a) at least one SAB member and (b) at least two non-SAB members who are experts in the area of the problem. The SAB will seek advice to determine potential non-SAB members who are internationally-recognized mathematical experts in the area of the problem. As part of this procedure, each component of a proposed solution under consideration shall be verified by one or more members of this special advisory committee. The special advisory committee will report within a reasonable time to the SAB. Based on this report and possible further investigation, the SAB will make a recommendation to the Directors. The SAB may recommend the award of a prize to one person. The SAB may recommend that a particular prize be divided among multiple solvers of a problem or their heirs. The SAB will pay special attention to the question of whether a prize solution depends crucially on insights published prior to the solution under consideration. The SAB may (but need not) recommend recognition of such prior work in the prize citation, and it may (but need not) recommend the inclusion of the author of prior work in the award. If the SAB cannot come to a clear decision about the correctness of a solution to a problem, its attribution, or the appropriateness of an award, the SAB may recommend that no prize be awarded for a particular problem. If new information comes to light, the SAB may (but will not necessarily) reconsider a negative decision to recommend a prize for a proposed solution, but only after an additional two-year waiting period following the time that the new information comes to light. The SAB has the sole authority to make recommendations to the Directors of the CMI concerning the appropriateness of any award and the validity of any claim to the CMI Millennium Prize. In the case of the P versus NP problem and the Navier-Stokes problem, the SAB will consider the award of the Millennium Prize for deciding the question in either direction. In the case of the other problems if a counterexample is proposed, the SAB will consider this counterexample after publication and the same two-year waiting period as for a proposed solution will apply. If, in the opinion of the SAB, the counterexample effectively resolves the problem then the SAB may recommend the award of the Prize. If the counterexample shows that the original problem survives after reformulation or elimination of some special case, then the SAB may recommend that a small prize be awarded to the author. The money for this prize will not be taken from the Millennium Prize Problem fund, but from other CMI funds. Any person who is not a disqualified person (as that term is defined in section 4946 of the Internal Revenue Code) in connection with the Institute, or a then serving member of the SAB, may receive the Millennium Prize. All decision-making procedures concerning the CMI Millennium Prize Problems are private. This includes the deliberations or recommendations of any person or persons CMI has used to obtain advice on this question. No records of these deliberations or related correspondence may be made public without the prior approval of the Directors, the SAB, and all other living persons involved, unless fifty years time have elapsed after the event in question. Please send inquiries regarding the Millennium Prize Problems to prize.problems@claymath.org. Revision of January 19, 2005 * History * Press statement * Press reaction * Publication Guidelines Return to top --Also, and this is important: if there is anything you see a vulnerability in my proof that makes it look like what I said is not true, or needs clarifying, perhaps maybe to people who are always nay saying, pointing a finger and exclaiming, You're wrong, here's why!, please tell me: For this to be true, this has to be true. You have accomplished this, so the next step is to do this. Here are M.I.T.'s accessibility report card: (these are for critiques of proof and ongoing discovery utilizes them). I have a little niece who is hearing impaired and she is my absolute angel. So this is an important one to me. 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I am making plans to contact other people who would like to join the Cause for Truth! P==NP campaign, so any critical comments to energize the troops. (oh, in case I forget, here is: sacook [at] cs [dot] toronto [dot] edu. MARTIN M. MUSATOV: m[dot]mm[at]vzw[dot]blackberry[dot]net === Subject: Re: P=NP Proof Published at CERN > familiar with the Internet...a huge+ Use TeX/LaTeX the way every does and has been doing since before there was an internet. Best way to get nicely readable math documents. Don't use evil corporate monopolies like MS or Google. Victor. -- Victor Eijkhout -- eijkhout at tacc utexas edu === Subject: Re: P=NP Proof Published at CERN familiar with the Internet...a huge+ Use TeX/LaTeX the way every does and has been doing > since before there > was an internet. Best way to get nicely readable math > documents. Don't use evil corporate monopolies like MS or > Google. Victor. > -- > Victor Eijkhout -- eijkhout at tacc utexas edu === Subject: Re: P=NP Proof Published at CERN <1izhuu1.yd67nr1ljknkeN%see@sig.for.address> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Configuration/CLDC-1.1 VendorID/105,gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) To spite technology in the face of ease of use is to spite your whole face and not just your nose. It is foolish to favor tradition for the sake of tradition, and I say this with all due respect to my peers and elders in this research. --Martin Musatov familiar with the Internet...a huge+ Use TeX/LaTeX the way every does and has been doing since before there > was an internet. Best way to get nicely readable math documents. Don't use evil corporate monopolies like MS or Google. Victor. > -- > Victor Eijkhout -- eijkhout at tacc utexas edu === Subject: Re: P=NP Proof Published at CERN posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 Firefox/3.0.10,gzip(gfe),gzip(gfe) > To spite technology in the face of ease of use is to spite your whole > face and not just your nose. It is foolish to favor tradition for the > sake of tradition, and I say this with all due respect to my peers and > elders in this research. --Martin Musatov Well, you decided to not favor tradition and all you got out of it was an unreadable file... I really hope the production of that unreadable file was made easy and comfortable through the use of tools with great ease-of-use and user-friendliness! :) -- m === Subject: Re: P=NP Proof Published at CERN <1izhuu1.yd67nr1ljknkeN%see@sig.for.address> posting-account=5t-ZfgkAAACU7ydoC4Cq-xVNAFsq481f Gecko/2009032802 Mandriva/1.9.0.8-1mdv2009.1 (2009.1) Firefox/3.0.8,gzip(gfe),gzip(gfe) > Use TeX/LaTeX the way every does and has been doing since before there > was an internet. Best way to get nicely readable math documents. Don't use evil corporate monopolies like MS or Google. But now yet better use TeXmacs, the free math text editor with ability to export into LaTeX. http://www.texmacs.org === Subject: Re: P=NP Proof Published at CERN > Use TeX/LaTeX the way every does and has been doing since before there > was an internet. Best way to get nicely readable math documents. Don't use evil corporate monopolies like MS or Google. But now yet better use TeXmacs, the free math text editor with ability > to export into LaTeX. http://www.texmacs.org--I will use what I use. I don't mix politics and math. *unless I they agree*