mm-4279 === Subject: topology question Need help with exercise 1.1 number 5 in C Patty's Foundations of Topology Show that if x=(x1,x2,....) and y=(y1,y2,...) where these are infinite tuples (i.e. not the 2tuples of the Cartesian plane but R^infinity - infinite Euclidean space) Show that if Summa of i=1 to infinity of xsubi^2 converges and Summa of i=1 to infinity of ysubi^2 converges then Summa of i=1 to infinity of absolute value of (xsubi times ysubi) converges. In other words if every element of the tuple squared and added up converges and there are two tuples then the absolute value of the tuples converges. Can someone steer me in the right direction? === Subject: Re: topology question It is enough to remember a trivial inequality: |xy| <= x^2 + y^2 > Need help with exercise 1.1 number 5 in C Patty's Foundations of Topology Show that if x=(x1,x2,....) and y=(y1,y2,...) where these are infinite > tuples (i.e. not the 2tuples of the Cartesian plane but R^infinity - > infinite Euclidean space) Show that if Summa of i=1 to infinity of xsubi^2 converges and Summa of i=1 > to infinity of ysubi^2 converges then > Summa of i=1 to infinity of absolute value of (xsubi times ysubi) converges. In other words if every element of the tuple squared and added up converges > and there are two tuples then the absolute value of the tuples converges. Can someone steer me in the right direction? === Subject: Re: topology question On Sun, 15 Jul 2007 18:52:29 -0700, mbcdba alt.math.undergrad: > Need help with exercise 1.1 number 5 in C Patty's Foundations of Topology > Show that if x=(x1,x2,....) and y=(y1,y2,...) where these > are infinite tuples [...] > Show that if Summa of i=1 to infinity of xsubi^2 converges > and Summa of i=1 to infinity of ysubi^2 converges then > Summa of i=1 to infinity of absolute value of (xsubi > times ysubi) converges. [...] > Can someone steer me in the right direction? Okay; you want to show that if SUM[i > 0; (x_i)^2] and SUM[i > 0; (y_i)^2] converge, then so does SUM[i > 0; |x_i y_i|]. Some hints: SUM[i > 0; (x_i)^2 + (y_i)^2] converges; why? (|x_i| - |y_i|)^2 >= 0 (why?), so |x_i y_i| <= ... ? Brian === Subject: Re: topology question 0; (x_i)^2] and > SUM[i > 0; (y_i)^2] converge, then so does > SUM[i > 0; |x_i y_i|]. Some hints: > This is a topology question? Nay, isn't it an important point for some vector spaces? > SUM[i > 0; (x_i)^2 + (y_i)^2] converges; why? > (|x_i| - |y_i|)^2 >= 0 (why?), so |x_i y_i| <= ... ? > Have you not shown that the dot or inner product not only converges, but converges absolutely? The same method works for integrals instead of sums? Thus arrise two questions. How to show that an absolutely converging sequence converges and how to show if integeral |f(x)| dx exists finitely, so does integral f(x) dx. === Subject: Re: topology question The sum of two converging series still converges - this ultimately because the limit of the sums is the sum of the limits. (|x_i|-|y_i|)^2>=0 since the difference of any two reals squared is non-negative. Thus |x_i|^2-2|x_i||y_i|+|y_i|^2>=0 so |x_i||y_i|<=(|x_i|^2+|y_i|^2)/2 and by the comparison test |x_i||y_i| converges. Any mis-steps in the above? > On Sun, 15 Jul 2007 18:52:29 -0700, mbcdba > alt.math.undergrad: > Need help with exercise 1.1 number 5 in C Patty's Foundations of Topology > Show that if x=(x1,x2,....) and y=(y1,y2,...) where these > are infinite tuples [...] > Show that if Summa of i=1 to infinity of xsubi^2 converges > and Summa of i=1 to infinity of ysubi^2 converges then > Summa of i=1 to infinity of absolute value of (xsubi > times ysubi) converges. [...] > Can someone steer me in the right direction? Okay; you want to show that if SUM[i > 0; (x_i)^2] and > SUM[i > 0; (y_i)^2] converge, then so does > SUM[i > 0; |x_i y_i|]. Some hints: SUM[i > 0; (x_i)^2 + (y_i)^2] converges; why? > (|x_i| - |y_i|)^2 >= 0 (why?), so |x_i y_i| <= ... ? Brian === Subject: Re: topology question On Sun, 15 Jul 2007 21:04:53 -0700, mbcdba alt.math.undergrad: > The sum of two converging series still converges - this ultimately because > the limit of the sums is the sum of the limits. > (|x_i|-|y_i|)^2>=0 since the difference of any two reals squared is > non-negative. > Thus |x_i|^2-2|x_i||y_i|+|y_i|^2>=0 > so >|x_i||y_i|<=(|x_i|^2+|y_i|^2)/2 and by the comparison test |x_i||y_i| > converges. > Any mis-steps in the above? Looks fine to me. Brian === Subject: Re: topology question Correction In other words if every element of the tuple squared and added up converges and there are two tuples then the absolute value of PRODUCT OF the tuples converges. > Need help with exercise 1.1 number 5 in C Patty's Foundations of Topology Show that if x=(x1,x2,....) and y=(y1,y2,...) where these are infinite > tuples (i.e. not the 2tuples of the Cartesian plane but R^infinity - > infinite Euclidean space) Show that if Summa of i=1 to infinity of xsubi^2 converges and Summa of > i=1 to infinity of ysubi^2 converges then > Summa of i=1 to infinity of absolute value of (xsubi times ysubi) > converges. In other words if every element of the tuple squared and added up > converges and there are two tuples then the absolute value of the tuples > converges. Can someone steer me in the right direction? > === Subject: Re: JSH: Math Wars, reconsidered <5fs5qeF3dh44iU1@mid.individual.net I suggest to you that some of them haven't quite stopped and that > descendants of those British lower classes not only continue to try at > times to turn themselves into something of an upper class in the > United States, but they follow bizarre and twisted rules which are > THEIR interpretations of upper class behavior. They believe that upper class members are above the law, will win at > any cost, and exploit the people beneath them with no mercy, and that > denial of this reality is just a sign of a lack of education and lower > class status. > Besides, I somehow suspect that Arturo Magidin is *not* one of the > descendants of those British lower classes. :-) > Jose Carlos Santos I'm talking about an explanation for extraordinary circumstances There is really nothing that extraordinary except the persistence of your delusions. === Subject: Re: JSH: Math Wars, reconsidered crank, and afterwards X is acknowledged to be a crank, I thought he already was... Make up your mind! can X >successfully sue Y for defamation of character? There is a precedent (of unsuccessful attempt to sue): http://en.wikipedia.org/wiki/Underwood Dudley#Lawsuit You can see Judge Posner's opinion on the dismissal here: http://www.law.emory.edu/7circuit/jan96/95-2282.html **************************************** Hello!! I didn?t know William Dilworth, the crank suing Dudley, was...an engineer!!! Of all the non-mathematician cranks put to work at imaginary nonsenses, precisely an engineer had to sue a mathematician for being called a crank...isn?t indeed Crankology 101 a compulsory subject in some engineering schools? As usual, most anticantorians (this is a name they love to call themselves) are not only cranks, but not even mathematicians....oh well. Tonio === Subject: Re: +1600 Solutions Manual to low cost Please help me, I want this ebook Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) Who can help send this ebook for me. nutchanonn[at]hotmail.com === Subject: solution manual I'm looking for solutions manual of the title Elementary Modern Physics by Paul A. Tyler. The ISBN: 0-87901-569-1. Please let know asap. BuiXui === Subject: solution manual Cc: phana@sbcglobal.net I'm looking for solution manual of the title Elementary Modern Physics by Paul A. Tyler. 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Cengal Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles (Instructor's Solutions Manual) Thermodyanamics of Turbomachinary 5E Time-Harmonic Electromagnetic Fields by Harrington solutions, 2001 Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas Vol 1 Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas Vol 2 Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2 problems) University Physics with Modern Physics (11th) by Hugh D. Young and Roger A. Freedman. Vector Calculus 3rd Ed. by Susan Jane Colley Vector Mechanics for engineers dynamics by beer 6th edition Vector Mechanics for engineers dynamics by beer 7th edition Vector Mechanics for engineers statics by beer 6th edition Vector Mechanics for engineers statics by beer 7th edition (nearly the same with edtion 8) Wireless Communications principles and practice 2nd Ed. by Theodore Rappaport 1996 === Subject: Re: Solution Manuals Available Now in PDF! 1) you only need to post that you have solution manuals once 2) this is not the alt.math.solution_manuals group - perhaps you should start one so those of us interested in *math* can post about math here. === Subject: Re: Hudreds and Hundreds of Solutions Manuals and Ebooks in all Subjects Yes contact me at thomchoo@hotmail.com. I can send it to you for $10. === Subject: I have the Instructors Solutions Manual for Thomas, Calculus, 11th Edition This is theInstructors Solutions Manual for Thomas, Calculus, 11th Edition. My price is $11. I only accept paypal. Samples available. If you are interested, contact me at amalm06@gmail.com === Subject: Instructors Solutions Manual for Hayt, Engineering Electromagnetics, 7th Ed This is the Instructors Solutions Manual for Hayt, Engineering Electromagnetics, 7th Edition. My price is $11. I only accept paypal. If you are interested, contact me at amalm06@gmail.com === Subject: Re: Instructors Solutions Manual for Hayt, Engineering Electromagnetics, 7th Ed > This is the Instructors Solutions Manual for Hayt, Engineering Electromagnetics, 7th Edition. My price is $11. I only accept paypal. If you are interested, contact me at amalm06@gmail.com You only need to post once, and really- why not form a separate group for solution manuals instead of spamming this group? === Subject: Sir Isaac Newton, has originated, inter-conversion of mass and energy, (E=mc2 ) Sir Isaac Newton, has originated, inter-conversion of mass and energy, (E=mc2 ) Newton has stated first of all about inter conversion of mass and energy. Einstein has derived first mathematical equation for the same. Newton [1] has quoted in his book OOpticksO in 1704 that Gross bodies and light are convertible into one another..., [ 1 ] Sir Isaac Newton, Opticks, pp. CVX (1704; reprinted by Dover Publications, Inc., New York, 1952). After about 200 years Einstein [2] derived mathematical equation for NewtonOs perception i.e. L =mc2 where L is light energy emitted when mass m is annihilated and c is speed of light. It is the rarest coincidence in between NewtonOs hypothesis and EinsteinOs mathematical derivation. [2] Einstein, A., Annalen der Physik 18, 639 (1905). Then from L =mc2 Einstein speculated E =mc2 For details you may like to visit http://www.ajayonline.us === Subject: Re: Sir Isaac Newton, has originated, inter-conversion of mass and energy, (E=mc2 ) Sir Isaac Newton, has originated, inter-conversion of mass and energy, > (E=mc2 ) Newton has stated first of all about inter conversion of mass and > energy. Einstein has derived first mathematical equation for the same. Newton [1] has quoted in his book .89uOpticks.89u in 1704 that > Gross bodies and light are convertible into one another..., True, but he had no formula, nor am I aware that he published any indication of why he believed what you have quoted. -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand.