mm-4449 === Subject: Electromagnetic Fields and Waves by Magdy Iskander === Subject: Solutions Manual to An Elementary Introduction to Mathematical Finance: Options and other Topics (2nd Ed., Sheldon M. Ross) I'm looking for Solutions manual for : An Elementary Introduction to Mathematical Finance: Options and other Topics (2nd Ed., Sheldon M. Ross) Please let me know if you have them. Transactions thru' paypal. sk168168atgmail.com === Subject: Re: Mathematical Solipsism I don't know why, but I must tell a joke: The dean of a small university wants to build a new faculty (Why? Eh, for the fame? Bugs me, it's a joke) and since it's a small university (I said that?!) they are short on money, and he asks a financial expert (who will probably charge more for his advice than is saved): Which kind of faculty will be least expensive? The expert: My second best suggestion would be a math faculty. Give them enough pencils and paper and a waste basket and they'll be the happiest guys on earth. And you can top that still?! Yes. Do a philosophy faculty and you can even spare the money for a waste basket. -- Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de order stormed the surface where chaos set norm had there always been balance? ...surely not therein lies the beauty === Subject: Re: Mathematical Solipsism >I don't know why, but I must tell a joke: The dean of a small university wants to build a new faculty >(Why? Eh, for the fame? Bugs me, it's a joke) and since >it's a small university (I said that?!) they are short on >money, and he asks a financial expert (who will probably >charge more for his advice than is saved): Which kind of >faculty will be least expensive? >The expert: My second best suggestion would be a >math faculty. Give them enough pencils and paper and >a waste basket and they'll be the happiest guys on earth. >And you can top that still?! >Yes. Do a philosophy faculty and you can even spare the >money for a waste basket. Believe I heard something similar recently.Nature abhors philosophers. ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. ~v~~ There is another way to analyse solipsism, which is curious in its generality and came up in the thread (Re: third believe system Re: Does Searle's Chinese Room argument imply that consciousness is non-scientific?). We came up with the consideration that IF we agree that thinking requires not only information processing but also context (semantics can not be created from grammar) than individual human can only think about objects included in his own context sphere, e.g. basically his body and its functions. Only within this sphere he can have physically relevant and in no way extrapolated or speculated states, that can be manipulated in the thinking process. When human appears to be thinking about objects outside of his bodily functions (which would be majority of thinking time of a modern human), he is importing context from the humanity external to him, e.g. he is not thinking (processing within context that he physically owns) but doing data-processing of irrelevant to him states no different from any computer. Information processing involved does not have contextual basis in his self. any information conceivable and have complete contextual basis for it is humanity rather than single human. Based on this context sphere approach, solipsism is correct (in terms of truth completely free from extrapolation). But because it is up to us how to define the boundaries of the context sphere, there can be different _levels_ of solipsism. It can be on a single ferment level, on a cell level, on a single human level, on a country level and finally on entire humanity level. Each of this solipsisms are correct for the type of answer that is defined withing its own context sphere. Depending on what is the level sufficient to describe the particular truth we are interested in, the answer will be available only to the entity that encompases corresponding context sphere. For example the true, free of extrapolation answers to the questions that can be defined only using human culture information will be available only to humanity as a whole rather than to single humans. Answers related to bodily functions or states of mind will be available only to each individual. Evgenij === Subject: Re: Mathematical Solipsism Technically the purpose of the post was not to analyze solipsism but to analyze mathematical mysticism as a variant of solipsism. > Mathematical Solipsism > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. ~v~~ There is another way to analyse solipsism, which is curious in its >generality and came up in the thread (Re: third believe system Re: Does >Searle's Chinese Room argument imply that consciousness is >non-scientific?). We came up with the consideration that IF we agree that thinking >requires not only information processing but also context (semantics can >not be created from grammar) than individual human can only think > about objects included in his own context sphere, e.g. basically his >body and its functions. > Only within this sphere he can have physically relevant >and in no way extrapolated or speculated states, that can be manipulated >in the thinking process. When human appears to be thinking about objects outside of his >bodily functions (which would be majority of thinking time of a modern >human), he is importing context from the humanity external to him, >e.g. he is not thinking (processing within context that he physically >owns) but doing data-processing of irrelevant to him states no different >from any computer. Information processing involved does not have >contextual basis in his self. any information conceivable and have complete contextual basis for it is >humanity rather than single human. Based on this context sphere approach, solipsism is correct >(in terms of truth completely free from extrapolation). But >because it is up to us how to define the boundaries of the >context sphere, there can be different _levels_ of solipsism. >It can be on a single ferment level, on a cell level, on a >single human level, on a country level and finally on entire >humanity level. Each of this solipsisms are correct for the type of answer >that is defined withing its own context sphere. Depending on what >is the level sufficient to describe the particular truth we are >interested in, the answer will be available only to the entity >that encompases corresponding context sphere. For example the true, free of extrapolation answers to the questions >that can be defined only using human culture information will be >available only to humanity as a whole rather than to single humans. > Answers related to bodily functions or states of mind will be >available only to each individual. Evgenij ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. ~v~~ Solipsism markes the transcendentally real limit to mathematical logic. It can be disposed of by abandoning transcendental realism. For example, we cannot say 'I, alone', for a singular is not countable. (You have read this idea here first. Do not use elsewhere without quoting this source, as this material is being used in a dissertation. John Jones 0ct 2007) === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. > ~v~~ Solipsism markes the transcendentally real limit to mathematical >logic. It can be disposed of by abandoning transcendental realism. For >example, we cannot say 'I, alone', for a singular is not countable. (You have read this idea here first. Do not use elsewhere without >quoting this source, as this material is being used in a dissertation. >John Jones 0ct 2007) I promise never to use it at all. ~v~~ === Subject: Re: Mathematical Solipsism Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. > ~v~~ Solipsism markes the transcendentally real limit to mathematical >logic. It can be disposed of by abandoning transcendental realism. For >example, we cannot say 'I, alone', for a singular is not countable. (You have read this idea here first. Do not use elsewhere without >quoting this source, as this material is being used in a dissertation. >John Jones 0ct 2007) I promise never to use it at all. ~v~~- Hide quoted text - - Show quoted text - I gave you a solution. You ignored it! Did you understand it? === Subject: Re: Mathematical Solipsism The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. This statement, in and of itself, is quite interesting. How is this established? Are you claiming it as an axiom or is it demonstrable? M === Subject: Re: Mathematical Solipsism > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. This statement, in and of itself, is quite interesting. How is this >established? Are you claiming it as an axiom or is it demonstrable? No, no, not at all. It's simply a comment directed at the historical assessment of the doctrine throughout the ages. It's not intended to be necessarily exhaustively correct. However it does turn out that every venue of science, from math to science, is a variant of some form of solipsism in the absence of any ability to demonstrate truth in fullly reduced mechanically exhaustive terms. ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. Well, what was known about Solipism though, is that The Liar's Paradox is closely related to the principle. Which is why Goedel worked on that to his theorems, and let cranks like Mathematicans, work on Euclid crank stuff. ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. Well, what was known about Solipism though, is that > The Liar's Paradox is closely related to the principle. > Which is why Goedel worked on that to his theorems, > and let cranks like Mathematicans, work on Euclid crank stuff. Nooo idear where you're going with this. Euclid wasn't a crank. Mathematicians aren't cranks. Can't answer for the rest. ~v~~ === Subject: Re: Mathematical Solipsism <97sqg39mtb2hcvipdk4ikgjgjhf7nhg017@4ax.com > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. Well, what was known about Solipism though, is that > The Liar's Paradox is closely related to the principle. > Which is why Goedel worked on that to his theorems, > and let cranks like Mathematicans, work on Euclid crank stuff. Nooo idear where you're going with this. Euclid wasn't a crank. That's relative as they say: Since his logic was invented for people with two points, two toes, a number two pencil, a mathematican, and no DVD. > Mathematicians aren't cranks. Can't answer for the rest. ~v~~- Hide quoted text - - Show quoted text - === Subject: Re: Mathematical Solipsism > Nooo idear where you're going with this. Euclid wasn't a crank. That's relative as they say: > Since his logic was invented for people with > two points, two toes, a number two pencil, > a mathematican, and no DVD. Actually Euclid's logic was invented for all time. ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. ~v~~ If we try to treat the human objectively we will observe egocentric behaviors universally; if not for the individual then for a slightly larger grouping of individuals. In that this human behavior destroys symmetry we are then forced to recover that symmetry at a rational level. Yet many do take this individualist view of reality and so deny an absolute reality. Clearly we each have a model for reality running through our heads and the acceptance that this model is errant is perhaps the stumbling point. We attach strongly to belief systems so much so that old systems are purveyed to this day and land us in the religious cultural wars of our time e.g. Iraq. Does instantiating some details help? Women in this country did not have the right to vote until a relatively short time (three or four generations) ago. What then are we doing in Iraq shoving our culture down their throats? Can this be addressed as an egocentric behavior? How do three branches of one religion (the Abrahamics) come to fight each other in what may turn into a world war? Because they exclude one another. Each has their one book that is the word of God. OK, it gets more complicated than that but as a simplified top layer this is accurate. The same characters and geography accross them. En masse egocentrism may not be the proper paradigm yet the effect is nearby. Especially humans engaged in a belief system en masse seem to have no problem adapting and absorbing it to a deep enough level for these systems to carry on for thousands of years. The social behavior of humans has to be addressed to get beneath your solipsistic thinking. The sad truth is that the human race falls short of the ideals that such a model assumes within its basis. -Tim === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. > ~v~~ If we try to treat the human objectively we will observe egocentric >behaviors universally; if not for the individual then for a slightly >larger grouping of individuals. In that this human behavior destroys >symmetry we are then forced to recover that symmetry at a rational >level. Yet many do take this individualist view of reality and so deny >an absolute reality. Clearly we each have a model for reality running >through our heads and the acceptance that this model is errant is >perhaps the stumbling point. We attach strongly to belief systems so >much so that old systems are purveyed to this day and land us in the >religious cultural wars of our time e.g. Iraq. Does instantiating some details help? Instantiating some details of what? All you have is some miscellaneous opinions problematically bearing on nothing I've said. > Women in this country did not >have the right to vote until a relatively short time (three or four >generations) ago. What then are we doing in Iraq shoving our culture >down their throats? Can this be addressed as an egocentric behavior? >How do three branches of one religion (the Abrahamics) come to fight >each other in what may turn into a world war? Because they exclude one >another. Each has their one book that is the word of God. OK, it gets >more complicated than that but as a simplified top layer this is >accurate. The same characters and geography accross them. En masse >egocentrism may not be the proper paradigm yet the effect is nearby. >Especially humans engaged in a belief system en masse seem to have no >problem adapting and absorbing it to a deep enough level for these >systems to carry on for thousands of years. The social behavior of >humans has to be addressed to get beneath your solipsistic thinking. >The sad truth is that the human race falls short of the ideals that >such a model assumes within its basis. Oooookay then. Moving right along to the next non sequitur. ~v~~ === Subject: Re: Mathematical Solipsism Mathematical Solipsism > ~v~~ Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. ~v~~ >If we try to treat the human objectively we will observe egocentric >behaviors universally; if not for the individual then for a slightly >larger grouping of individuals. In that this human behavior destroys >symmetry we are then forced to recover that symmetry at a rational >level. Yet many do take this individualist view of reality and so deny >an absolute reality. Clearly we each have a model for reality running >through our heads and the acceptance that this model is errant is >perhaps the stumbling point. We attach strongly to belief systems so >much so that old systems are purveyed to this day and land us in the >religious cultural wars of our time e.g. Iraq. >Does instantiating some details help? Instantiating some details of what? All you have is some miscellaneous > opinions problematically bearing on nothing I've said. > Women in this > country did not >have the right to vote until a relatively short time (three or four >generations) ago. What then are we doing in Iraq shoving our culture >down their throats? Can this be addressed as an egocentric behavior? >How do three branches of one religion (the Abrahamics) come to fight >each other in what may turn into a world war? Because they exclude one >another. Each has their one book that is the word of God. OK, it gets >more complicated than that but as a simplified top layer this is >accurate. The same characters and geography accross them. En masse >egocentrism may not be the proper paradigm yet the effect is nearby. >Especially humans engaged in a belief system en masse seem to have no >problem adapting and absorbing it to a deep enough level for these >systems to carry on for thousands of years. The social behavior of >humans has to be addressed to get beneath your solipsistic thinking. >The sad truth is that the human race falls short of the ideals that >such a model assumes within its basis. Oooookay then. Moving right along to the next non sequitur. > Ignoring the response? Can't handle the fact that other people are right and you are wrong? === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. > ~v~~ If we try to treat the human objectively we will observe egocentric >behaviors universally; if not for the individual then for a slightly >larger grouping of individuals. In that this human behavior destroys >symmetry we are then forced to recover that symmetry at a rational >level. Yet many do take this individualist view of reality and so deny >an absolute reality. Clearly we each have a model for reality running >through our heads and the acceptance that this model is errant is >perhaps the stumbling point. We attach strongly to belief systems so >much so that old systems are purveyed to this day and land us in the >religious cultural wars of our time e.g. Iraq. Does instantiating some details help? > Instantiating some details of what? All you have is some miscellaneous > opinions problematically bearing on nothing I've said. > Women in this > country did not >have the right to vote until a relatively short time (three or four >generations) ago. What then are we doing in Iraq shoving our culture >down their throats? Can this be addressed as an egocentric behavior? >How do three branches of one religion (the Abrahamics) come to fight >each other in what may turn into a world war? Because they exclude one >another. Each has their one book that is the word of God. OK, it gets >more complicated than that but as a simplified top layer this is >accurate. The same characters and geography accross them. En masse >egocentrism may not be the proper paradigm yet the effect is nearby. >Especially humans engaged in a belief system en masse seem to have no >problem adapting and absorbing it to a deep enough level for these >systems to carry on for thousands of years. The social behavior of >humans has to be addressed to get beneath your solipsistic thinking. >The sad truth is that the human race falls short of the ideals that >such a model assumes within its basis. > Oooookay then. Moving right along to the next non sequitur. Ignoring the response? Can't handle the fact that other people are right and >you are wrong? Of course I can't. Just haven't run into any. ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. > ~v~~ Truth is in the eye of the beholder. Your theory is bunko, all sloppieism. Well I certainly appreciate your opinion. However your demonstration for it seems somewhat defective, read NON EXISTENT. In science we prefer to support opinions with demonstrations of truth. ~v~~ === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. ~v~~ >Truth is in the eye of the beholder. Your theory is bunko, all >sloppieism. Well I certainly appreciate your opinion. However your demonstration > for it seems somewhat defective, read NON EXISTENT. In science we prefer to support opinions with demonstrations of truth. > your sloppieism is not science, but contaminated bunko. Truth is relative. === Subject: Re: Mathematical Solipsism > Mathematical Solipsism > ~v~~ > Conventional solipsism is a logical philosophy whose underlying views > apply equally to mathematical philosophies of neopythagoreanism and > neoplatonism as well as mathematical realism and empiricism generally. > The well established philosophical principle of solipsism is that only > the individual is or can be demonstrated to exist. But the problem is > that if this principle were actually demonstrably true it would also > make it false because the truth established would ipso facto make > the principle beyond control of any individual. > Nobody really thinks solipsism is true. But the difficulty is no one > can prove or disprove the concept because no one can prove the > foundations of truth in absolute, necessary, and universal terms. > ~v~~ Truth is in the eye of the beholder. Your theory is bunko, all >sloppieism. > Well I certainly appreciate your opinion. However your demonstration > for it seems somewhat defective, read NON EXISTENT. > In science we prefer to support opinions with demonstrations of truth. your sloppieism is not science, but contaminated bunko. Truth is relative. You have a relative named Truth? How nice. ~v~~ === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers >In ZFC, with standard definitions of the real, rational, and >irrational numbers, let p_i be an irrational number between zero >and one for i from a suitably large well-ordered index set X. Okay, let me restate what I think you are saying explicitly, and > correct me if you mean something else. Are you saying that you are > well ordering the irrationals? Okay, let's say so. Now this index > set X of your's, I presume that this is merely a subset of ordinals > large enough to contain the irrationals, is that right? He won't say exactly, except that it is a sufficiently large > ordinal, whatever that means. In other > words, p_i is an irrational for any given ordinal i where i is an > ordinal less than the cardinality of the irrationals. Is this > correct? > With the well-ordering of the index set, let the i'th element p_{i+1} >be an irrational number between zero and p_i... Whoa, whoa, whoa. I thought p_i was the i-th element. And how do you > know that p_i+1 is less than p_i? Nothing in the well ordering > requires this. You have not shown that there even exists an i such > that p_i+1 < p_i. >where i+1 is the least element of the well-ordering X_i set minus i... Huh? Isn't the i+1 simply the next ordinal after i? And what is this > X_i? I thought X was the index set; how do you define X_i? Can you start again, explain each step here? I tried to get him to be precise at each step, step by step. He won't > do it. He'll only explain in such a way as to come back around full > circle (or with added orbits of confusion) to the mishmosh > formulations he started with. MoeBlee I answered Moe's questions and he denied they were so (eg C is a particular satisfying a property, F is the collection of all such functions satisfying said property.) For example he asks for a function on ordinals for transfinite recursion and I described it in terms of functions on zero, successor, and limit ordinals as is accepted in various references, compositely a single function defined on ordinals in terms of course-of-values as indicated. In terms of which ordinal X is, it is sufficiently large. I explain in such a way as to come back around full circle to the formulations I started with. If you have a question that's not already answered I'd to be happy to answer it. I'll be happy to make neat the proof, currently I'm still wondering about various objections and questions about the use of transfinite induction to make statements about more than countably members of a more than countable set, in ZFC. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > If you have a question that's not already answered I'd to be happy to > answer it. I'll be happy to make neat the proof, currently I'm still > wondering about various objections and questions about the use of > transfinite induction to make statements about more than countably > members of a more than countable set, in ZFC. I had some questions about your proof that I did not follow, but I did not see you respond to them. Are they responded to elsewhere? Jonathan Hoyle http://www.jonhoyle.com === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > I answered Moe's questions and he denied they were so (eg C is a > particular satisfying a property, F is the collection of all such > functions satisfying said property.) Then define C without mentioning F already! Please, stop saying that you've done this and that when you haven't. Just give us a definition of C in terms of NOTHING but previously defined terms of ZFC and the X we've got on the table now. Nothing else is on the table but previously defined terms of ZFC and X. So now define C in terms of only what is on the table. Put up or shut up, please. > For example he asks for a > function on ordinals for transfinite recursion and I described it in > terms of functions on zero, successor, and limit ordinals as is > accepted in various references, compositely a single function defined > on ordinals in terms of course-of-values as indicated. In terms of > which ordinal X is, it is sufficiently large. We'll get to that later, after you've defined the G in your transfinite recursion. But first let's get your definition of C. Then we'll move on to your F, then to your G, then to your transfinite recursion. MoeBlee === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > Now, back to the argument at hand, it has to do with well-ordering a > subset of the irrationals. As described above using transfinite > induction, or a transfinite recursion schema indicating a well- > ordering of a subset of the irrationals, there is thus described in > ZFC using standard definitions of the irrational numbers a set of > irrationals. This set, which is constructible in ZFC via the well- > ordering principle, if it can't be uncountable, has that there aren't > uncountably many irrationals. Otherwise, it can be uncountable, in > ZFC, and is constructed so as to be. That done, it is illustrated > that due the denseness of the rationals in the reals, and reverse > normal ordering on the set, that for each element of the uncountable > set of irrationals there exists a particular, distinct rational > number. Otherwise the rationals aren't dense in the reals. Then, via Cantor-Schroeder-Bernstein and a trivial injection the other > way, there is a bijection between the irrationals and rationals, due > to the denseness of each of the rationals and irrationals in the > reals. Apart from being difficult to follow (as usual), this sounds a lot like Tony's argument from a few months back: Since between every two rationals there exists an irrational, and between every two irrationals there exists a rational, therefore the real number line must be composed of alternating rational and irrational number points. Or perhaps this is your way of saying that the rationals and irrationals are equally dense in the reals? === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > Now, back to the argument at hand, it has to do with well-ordering a > subset of the irrationals. As described above using transfinite > induction, or a transfinite recursion schema indicating a well- > ordering of a subset of the irrationals, there is thus described in > ZFC using standard definitions of the irrational numbers a set of > irrationals. This set, which is constructible in ZFC via the well- > ordering principle, if it can't be uncountable, has that there aren't > uncountably many irrationals. Otherwise, it can be uncountable, in > ZFC, and is constructed so as to be. That done, it is illustrated > that due the denseness of the rationals in the reals, and reverse > normal ordering on the set, that for each element of the uncountable > set of irrationals there exists a particular, distinct rational > number. Otherwise the rationals aren't dense in the reals. Then, via Cantor-Schroeder-Bernstein and a trivial injection the other > way, there is a bijection between the irrationals and rationals, due > to the denseness of each of the rationals and irrationals in the > reals. Apart from being difficult to follow (as usual), this sounds > a lot like Tony's argument from a few months back: > Since between every two rationals there exists an > irrational, and between every two irrationals there exists > a rational, therefore the real number line must be composed > of alternating rational and irrational number points. Or perhaps this is your way of saying that the rationals > and irrationals are equally dense in the reals? In a way, yes. Much further discussion of NCD2 sets in the reals as I call them can be found on sci.math/sci.logic archives. In a way, no. It's moreso a way of saying that ZF is inconsistent so to re-Vitali- ize measure theory. Infinite sets are equivalent. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > There are several tell-tale indicators of crankiness; see: > http://en.wikipedia.org/wiki/Crank_%28person%29 > http://tinyurl.com/8hah7 Consider the physical universe, and map mathematical objects to > physical objects. Then, (all) functions among those represent > physical objects, as do functions among those, ad infinitum. > Then, there are infinitely many objects in the universe, ... How do you know the physical universe is infinite? Or not? Do you have a mathematical argument for this, or a physical argument? Your realizable evidence is no such thing. > ... which mathematically is its own powerset. > Then, there is realizable evidence (contrary evidence) > that it is reasonable to discredit the powerset result. In order for an infinite set to be its own powerset, it would have to contain members that are themselves sets (permutations) of objects already in the set. How is this possible using physical objects? How is an infinite set of objects its own powerset? How does this work, since it contradicts the elementary proof that no set bijects with its own powerset? Are you assuming some set theory other than ZFC? === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > There are several tell-tale indicators of crankiness; see: > http://en.wikipedia.org/wiki/Crank_%28person%29 > http://tinyurl.com/8hah7 Consider the physical universe, and map mathematical objects to > physical objects. Then, (all) functions among those represent > physical objects, as do functions among those, ad infinitum. > Then, there are infinitely many objects in the universe, ... How do you know the physical universe is infinite? > Or not? Do you have a mathematical argument for this, > or a physical argument? Your realizable evidence is > no such thing. ... which mathematically is its own powerset. > Then, there is realizable evidence (contrary evidence) > that it is reasonable to discredit the powerset result. In order for an infinite set to be its own powerset, it > would have to contain members that are themselves > sets (permutations) of objects already in the set. > How is this possible using physical objects? How is an infinite set of objects its own powerset? > How does this work, since it contradicts the elementary > proof that no set bijects with its own powerset? Are you assuming some set theory other than ZFC? It's a mathematical argument from that given a set of physical objects, the set of functions between them, (which would be elementarily greater in cardinality in ZF as finite or infinite), exactly represent physical objects, as do those of theirs etcetera ad infinitum. Then, the universe contains all of them. It basically recognizes the belief that there is a physical universe, which by definition contains everything, in reality because the mathematical universe is denied in regular set theory, to illustrate why in terms of a reasonable foundation of mathematics to model physics that denial of a universe is absurd in cosmology. Consider Kolker, his stated opinion is No opinion. Period., and he readily dispenses with his opinion. Only the null axiom theory could be the T.o.E. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > What's your opinion about the topic under discussion: is the > specified transfinite recursion schema not defined for ordinals up to > the cardinality of the irrationals? If it's not, the irrationals > aren't uncountable. If it is, they aren't either. Your attempted proof that the irrationals are uncountable I agree with MoeBlee that you are not properly defining the limit ordinals upon which you base your theorem. You use an ordinal X that is sufficiently large. So how is X defined, and what is it exactly? You still have not told us. === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > You use an ordinal X that is sufficiently large. So how > is X defined, and what is it exactly? You still have not > told us. I assume that by sufficiently large, RF means an ordinal alpha such that there exists a injection from the set of irrational reals to alpha. But neither RF nor anyone else can calculate alpha. Why not? It is all due to the undecidablity of the Continuum Hypothesis. In ZFC+CH, aleph_1 (i.e., omega_1) is sufficiently large, but in ZFC+~CH, aleph_1 isn't sufficiently large. And it's impossible to determine whether aleph_2, aleph_3, aleph_omega_1, etc., are sufficiently large, since there is no upper limit on the size of the continuum in ZFC+~CH. So neither RF nor any professional mathematician, can give an explicit ordinal alpha that is sufficiently large that there exists an injection from the set of irrationals into alpha. === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers You use an ordinal X that is sufficiently large. So how > is X defined, and what is it exactly? You still have not > told us. I assume that by sufficiently large, RF means an ordinal alpha > such that there exists a injection from the set of irrational reals > to alpha. But neither RF nor anyone else can calculate alpha. Why not? It > is all due to the undecidablity of the Continuum Hypothesis. In ZFC+CH, aleph_1 (i.e., omega_1) is sufficiently large, but in > ZFC+~CH, aleph_1 isn't sufficiently large. And it's impossible > to determine whether aleph_2, aleph_3, aleph_omega_1, etc., > are sufficiently large, since there is no upper limit on the size > of the continuum in ZFC+~CH. So neither RF nor any professional mathematician, can give an > explicit ordinal alpha that is sufficiently large that there exists > an injection from the set of irrationals into alpha. I think that was implicit (well-known). Where there are uncountably many irrationals, say c many where c is the cardinality of the continuum, and the set P can be constructed with that many elements, a striking point is that there is a distinct rational for each irrational in that set. Where P can't be constructed with that many elements, the irrationals aren't uncountable, else there is a segment of the continuum for further division, and it can be, thus they aren't. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > What's your opinion about the topic under discussion: is the > specified transfinite recursion schema not defined for ordinals up to > the cardinality of the irrationals? If it's not, the irrationals > aren't uncountable. If it is, they aren't either. Your attempted proof that the irrationals are uncountable > I agree with MoeBlee that you are not properly defining > the limit ordinals upon which you base your theorem. You use an ordinal X that is sufficiently large. So how > is X defined, and what is it exactly? You still have not > told us. Sure I did, X is any uncountable ordinal equivalent (equipollent) to the irrationals. Pick one, I don't care which it is, as long as it has uncountably many elements in ZFC, and is not equivalent to a cardinal greater than that of the irrationals, so an uncountable set is constructed. The limit ordinals are already defined as those (infinite) ordinals with no predecessors. Then, the values of the uncountable set containing ordered pairs with an element p_lambda for limit ordinals is described in a manner of course-of-values as Suppes indicates in the chapter of his axiomatic set theory about transfinite induction. If there are uncountably many irrationals, then as the irrationals are dense in the reals: for any interval there are that many. So, there can be selected (in ZFC) that many as elements of an uncountable set P. Then, for each p_i E P, as shown above, as the rationals are dense in the reals: there exists a distinct rational q_i for each p_i. An alternative proof from last year is sketched in the reference, again leading to perceived internal inconsistencies in ZFC, and/or the standard definitions of the real, rational, or irrational numbers, although the other proof doesn't use much set theory, particularly not trans-finite set theoretic machinery, instead simply using ordering properties in trichotomy of the reals and proof via contradiction using properties of the real, rational, and irrational numbers. In a separate context with the notion that incompleteness entails unknown axioms, if there are unknown (anonymous) axioms deciding statements that are undecided by the non-anonymous objects of the theory, then the theory isn't recursively axiomatized. I borrowed a copy of Suppes' axiomatic set theory here, Davis' The Undecidable and the proceedings of symposia in pure mathematics volume XIII part I. So, I am enjoying reading these. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > You use an ordinal X that is sufficiently large. So how > is X defined, and what is it exactly? You still have not > told us. Sure I did, X is any uncountable ordinal equivalent (equipollent) to > the irrationals. You wouldn't say that previously. > Pick one, I don't care which it is, as long as it > has uncountably many elements in ZFC, and is not equivalent to a > cardinal greater than that of the irrationals, so an uncountable set > is constructed. The cardinality of the set of real numbers meets that description, just as I suggested about two weeks ago. > The limit ordinals are already defined as those > (infinite) ordinals with no predecessors. With no IMMEDIATE predecessors. Yes, we know that. > Then, the values of the > uncountable set containing ordered pairs with an element p_lambda for > limit ordinals is described in a manner of course-of-values as > Suppes indicates in the chapter of his axiomatic set theory about > transfinite induction. You gave a course of values schema, but you must first CORRECTLY define your 'G'. And just saying over and over again that it's G1, G2 and G3 is not what is needed. > [...] > I borrowed a copy of Suppes' axiomatic set theory here, Great! (Just a note: You can make some his stuff more streamlined just by not allowing urelements as he does; they just clutter some of the formulations. Just take the axiom of extensionality as universal, then derive existence of an empty set from the axiom schema of separation and the uniqueness of an empty set from extensionality, and you're all fixed up without annoying urelements. Also, given an obvious adjustment to his definition of 'ordinal', the axiom of regularity that he brings out right away is not needed until much later. Other than that, his trail of theorems and definitions is splendid.) MoeBlee === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > The limit ordinals are already defined as those > (infinite) ordinals with no predecessors. With no IMMEDIATE predecessors. Yes, we know that. Except that 'infinite' is not part of the definition. The definition is: L is a limit ordinal <-> (L is an ordinal & ~L=0 & ~Ex(x is an ordinal & L=x+)) MoeBlee === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > What's your opinion about the topic under discussion: is the > specified transfinite recursion schema not defined for ordinals up to > the cardinality of the irrationals? If it's not, the irrationals > aren't uncountable. If it is, they aren't either. Your attempted proof that the irrationals are uncountable > I agree with MoeBlee that you are not properly defining > the limit ordinals upon which you base your theorem. You use an ordinal X that is sufficiently large. So how > is X defined, and what is it exactly? You still have not > told us. I suggested that he might as well take X to be the cardinality of the set of real numbers. So, suppose he does that or suppose he just says X is an arbitrary uncountable ordinal. Fine. But then his next step is to introduce F and C, which he defines by defining each in terms of the other. If he can define one of them and then the other, then fine, his argument can then continue. But his argument is stopped when he can't define his F and C without defining them in terms of each other. MoeBlee === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > There are several tell-tale indicators of crankiness; see: > http://en.wikipedia.org/wiki/Crank_%28person%29 > http://tinyurl.com/8hah7 > See also: > http://en.wikipedia.org/wiki/Duck_test elements, as are sets. Are not proper classes defined by their > elements, containing some specified elements, as are sets, similarly > walking, quacking, etcetera? I meant the Duck Test to be applied to people, not to sets or classes. === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > There are several tell-tale indicators of crankiness; see: > http://en.wikipedia.org/wiki/Crank_%28person%29 > http://tinyurl.com/8hah7 > See also: > http://en.wikipedia.org/wiki/Duck_test elements, as are sets. Are not proper classes defined by their > elements, containing some specified elements, as are sets, similarly > walking, quacking, etcetera? I meant the Duck Test to be applied to people, not to sets or > classes. That's funny, I'm applying it to sets compared to proper classes. So, is it a reasonable form of argument? Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > There are several tell-tale indicators of crankiness; see: > http://en.wikipedia.org/wiki/Crank_%28person%29 > http://tinyurl.com/8hah7 > See also: > http://en.wikipedia.org/wiki/Duck_test > elements, as are sets. Are not proper classes defined by their > elements, containing some specified elements, as are sets, similarly > walking, quacking, etcetera? > I meant the Duck Test to be applied to people, not to sets or > classes. That's funny, I'm applying it to sets compared to proper classes. So, is it a reasonable form of argument? It is a reasonable form of inductive argument. Thus, if a thing x has a number of properties that all things Y have, then there is some reason to believe that x is a Y. But if you have a clear argument that establishes x is not a Y, then you would be foolish to think that it is, on the basis of the duck argument. Now, the duck argument works in the case David suggests. You have a number of traits that suggest you are a crank. There is no clear argument that establishes you are not a crank. Thus, we conclude that there is reason to believe you are a crank. None of this applies to the set/class distinction. A proper class is *by definition* not a set, and thus it is silly to point to similarities and conclude that it is a set. On the other hand, this silly argument *is* relevant. It is more evidence of general crankiosity. -- Jesse F. Hughes Besides, discoverers are too proud to kiss butt. Indiana Jones would never kiss some academic's ass to get published, and neither will I. --James Harris === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers <871wc19uhu.fsf@phiwumbda.org > There are several tell-tale indicators of crankiness; see: > http://en.wikipedia.org/wiki/Crank_%28person%29 > http://tinyurl.com/8hah7 > See also: > http://en.wikipedia.org/wiki/Duck_test > elements, as are sets. Are not proper classes defined by their > elements, containing some specified elements, as are sets, similarly > walking, quacking, etcetera? > I meant the Duck Test to be applied to people, not to sets or > classes. That's funny, I'm applying it to sets compared to proper classes. So, is it a reasonable form of argument? It is a reasonable form of inductive argument. Thus, if a thing x has > a number of properties that all things Y have, then there is some > reason to believe that x is a Y. But if you have a clear argument that establishes x is not a Y, then > you would be foolish to think that it is, on the basis of the duck > argument. Now, the duck argument works in the case David suggests. You have a > number of traits that suggest you are a crank. There is no clear > argument that establishes you are not a crank. Thus, we conclude that > there is reason to believe you are a crank. None of this applies to the set/class distinction. A proper class is > *by definition* not a set, and thus it is silly to point to > similarities and conclude that it is a set. On the other hand, this silly argument *is* relevant. It is more > evidence of general crankiosity. -- > Jesse F. Hughes > Besides, discoverers are too proud to kiss butt. Indiana Jones would > never kiss some academic's ass to get published, and neither will I. > --James Harris A set is a collection defined by its elements, a proper class is a collection defined by its elements. A set has a member of relation defined for its elements, a proper class has a member of relation defined for its elements. (It does, an element, a set, of a proper class is a member.) A set has a subset relation defined for its subsets, a proper class has a subset relation defined for its subclasses. (It does, a given collection of elements, sets, of a proper class is a subclass or not.) Those properties completely describe a set, a set is defined by its elements. In this context, in analogy to, say, the central dogma of molecular biology, you say a proper class has the exact same genome as a duck, and is defined to be not a duck, where a duck is defined by its genome. So, basically you take a duck and cut out its quacker and lop off its feet and say it's not a duck. It's still a duck, albeit a mutilated one, naturally quacking and walking. It's silly to point to no dissimilarities, except that proper classes as sets make ZF(C) inconsistent, and call them different. There are few so silly as those who blind themselves to see. Where the constructs under consideration (such as the collection of all ordinals, collection of all sets, eg universe) are deemed by many to exist a priori, in a regular (well-founded) set theory they can't exist. To acknowledge their existence and use them with sets, and deny them set-hood, that's not set theory. I suggest that you expand your comprehension. However, consider this, if you expand comprehension beyond ZFC's, then the collection of sets that was ZFC is the Russell set and irregular. ZFC is inconsistent. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers A set is a collection defined by its elements, a proper class is a > collection defined by its elements. A set has a member of relation > defined for its elements, a proper class has a member of relation > defined for its elements. (It does, an element, a set, of a proper > class is a member.) A set has a subset relation defined for its > subsets, a proper class has a subset relation defined for its > subclasses. (It does, a given collection of elements, sets, of a > proper class is a subclass or not.) Those properties completely describe a set, a set is defined by its > elements. Bull. The properties that completely define a set are given by the axioms of the theory at hand. How about this property? Every set is a member of some class. No class is a member of any class. > I suggest that you expand your comprehension. However, consider this, > if you expand comprehension beyond ZFC's, then the collection of sets > that was ZFC is the Russell set and irregular. ZFC is inconsistent. Right. But you have never given a proof of this inconsistency, primarily because you are incapable of proving *anything*. But you're not a crank, oh no. -- Damn John Jay. Damn everyone who won't damn John Jay. Damn everyone who won't put lights in his windows and sit up all night damning John Jay. -- Political graffiti from late 18th c. Boston === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > First Postulate: To draw a line from any point to any point. > To me, this is a bit vague. I agree. It's totally vague. It's not even a sentence. It's a desideratum, a goal for a task, like you might include as a comment in the preface to a software algorithm. For example, given two positive integers, to compute their greatest common divisor. But even as a goal, it's vague, as you explain. > if between every two points there exists another point, then a > line must be dense and consist of infinitely many points. I agree about the infinite-many-points remark. But the word dense is defined in a metric space, not in a geometry, so what you've said so-far makes no sense, since all you have is a geometry, not a metric space. Euclid didn't define any metric as far as I know, since the concept hadn't yet been conceived way back then. Now the question arises whether the axioms of Euclid, plus the choice of one particular line segment as a unit interval (equivalently choosing two distinct points as unit distance from each other), uniquely defines a metric space. I think so, but I'm not sure. Can somebody verify this conjecture? If so, then it must be the Euclidean metric, the usual metric on R^2 or R^3, and then per that metric ... um ... you still have a problem, that dense is a relation between two sets, not a property of a single set. One set is dense in another. So what do you really mean? I'm guessing that you mean that every point is a limit point per that metric, i.e. for each point the greatest lower bound on distances to other points is zero. Is that what you meant to say? Now there's a concept of nowhere dense, which seems to imply there's a meaning of dense that applies to a single set, or to a point of a set (the point is dense at that point), but I can't find the definition via Google search. Maybe that meaning of dense is what I defined in the previous paragraph, in which case I retract my quibble. Can an expert on this jargon please find the definition if it exists? > But still, that doesn't imply that a line must have _uncountably_ > many points. I think that's correct. Euclid's axioms seem to imply only constructable points (from whatever points we start with to generate a given geometry), and the constructable points are in fact countably infinite if the starting points were either finite or countably infinite. I think we may interpret the axioms of Euclid to imply that for any two distinct points there is a unique (closed) line segment between the two points (and also the two half-open and also the one open line segments too, by omitting one or both endpoints). With that accepted, we can now define the word convex entirely in Euclidean terms. (A set of points S is convex if for each pair of distinct points in S p1,p2 the line segment p1,p2 is a subset of S.) Then a single new axiom should suffice to generate uncountably infinite points in any geometry that contains at least two points: - Every convex subset of a line is either - a line segment (which may be open or closed or half-open either way), or - a ray (which may extend in either direction from its starting point, and may be open or closed at that starting point), or - the whole line. That axiom basically establishes a bijection between points on a line and Dedekind cuts, thereby giving us Cantor's uncountable reals along any line. Expert please, am I correct, or is that axiom not enough? > (Of course not, since uncountability didn't exist in Euclid's day.) But if a single new axiom, expressed in Euclid's own notational conventions, is sufficient to generate Dedekind cuts hence reals, then I think your remark is moot. > Indeed, recall that Euclid dealt mainly with constructions. I fail > to see how any of Euclid's axioms imply the existence of any > segment whose length is not a constructible number, such as cbrt(2) > (Doubling the Cube) or pi (Squaring the Circle). So Euclid's Axioms > imply the existence of only countably many points. Agreed, but see how easy it is to add just one more axiom, which would have seemed obvious (even moreso than the parallel postulate), to yield Cantor's uncountable reals! So I believe the geometry that Euclid really believed in was in fact Cantor's system. Is there anyone here who takes the opposite position, that Euclud would have accepted a partition of a line into two convex rays for which there was no point whatsoever between them? > Fifth Axiom: The whole is greater than the part. Clearly he's talking about measure (length) of line segments, not number of points in line segments. After all he devised an elementary construction to produce a bijection between any two (closed) line segments. > So where does one get the idea that there exist uncountably many > points anyway? Ask any schoolkid: My axiom is obviously true about realworld lines, right? > The Ruler Postulate clearly states that there exists a bijection > between the set of real numbers and the set of points on a line, I think my convex-subset postulate is more intuitively obvious. Back to Euclid without my extra postulate: > In the model of geometry in which only constructable points > exist, circles may exist, but a segment of measure pi doesn't > (Squaring the Circle). Indeed, in that system, a *curve* of arc-length pi does exist, but a *line-segment* of (arc-)length pi does not exist, assuming you start with just one origin point plus one extra point unit distance away for each dimension of the space, to generate the geometry via construction. (Of course if you *start* with three points, 0 1 and pi along a single line, then you already have a line segment of exactly pi, ) === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers On Oct 10, 2:21 am, rem6...@yahoo.com (Robert Maas, see http://tinyurl.com/uh3t) > if between every two points there exists another point, then a > line must be dense and consist of infinitely many points. I agree about the infinite-many-points remark. > But the word dense is defined in a metric space, not in a > geometry, so what you've said so-far makes no sense, since all you > have is a geometry, not a metric space. Euclid didn't define any > metric as far as I know, since the concept hadn't yet been > conceived way back then. I'm using the definition of dense that only requires an order, not a full metric. http://en.wikipedia.org/wiki/Dense_order In mathematics, a partial order on a set X is said to be dense (or dense-in-itself) if, for all x and y in X for which x < y, there is a z in X such that x < z < y. > I think we may interpret the axioms of Euclid to imply that for any > two distinct points there is a unique (closed) line segment between > the two points (and also the two half-open and also the one open > line segments too, by omitting one or both endpoints). With that > accepted, we can now define the word convex entirely in Euclidean > terms. (A set of points S is convex if for each pair of distinct > points in S p1,p2 the line segment p1,p2 is a subset of S.) Then a > single new axiom should suffice to generate uncountably infinite > points in any geometry that contains at least two points: > - Every convex subset of a line is either > - a line segment (which may be open or closed or half-open either way), > or > - a ray (which may extend in either direction from its starting > point, and may be open or closed at that starting point), > or > - the whole line. > That axiom basically establishes a bijection between points on a > line and Dedekind cuts, thereby giving us Cantor's uncountable reals > along any line. > Expert please, am I correct, or is that axiom not enough? I see what you mean. If one can prove that it is impossible for the union of two half-lines (i.e., two _open_ rays) to be a full line, then there must be uncountably many points. Surprisingly, even Hilbert's refinement of Euclidean geometry says nothing about this. Once again, there's his Line Completeness Axiom, but that doesn't seem to me to say anything about the union of two open rays not being the entire line. Here's a link to Euclid's and Hilbert's axioms: http://www.friesian.com/space.htm === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > There's a trivial injection from the rationals to a subset of the > irrationals. Correct. x -> x+sqrt(2) will do nicely for example. > Thus, with an injection either way, ... What do you mean either way?? There is an injection in only one direction, not the reverse. > the Cantor-Bernstein theorem gives a bijection Nope. To apply that theorem you would need injections both ways. You have an injection only in one direction. === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers On Oct 10, 1:23 am, rem6...@yahoo.com (Robert Maas, see http://tinyurl.com/uh3t) > There's a trivial injection from the rationals to a subset of the > irrationals. Correct. x -> x+sqrt(2) will do nicely for example. Thus, with an injection either way, ... What do you mean either way?? There is an injection in only one > direction, not the reverse. the Cantor-Bernstein theorem gives a bijection Nope. To apply that theorem you would need injections both ways. > You have an injection only in one direction. Excuse me, you seem to be somewhat out of touch with the current discussion. Using ZFC an injection is constructed from an uncountable set of irrationals to a subset of the rationals. Ross -- Finlayson Consulting === Subject: Re: Rational numbers, irrational numbers: each dense in real numbers > you seem to be somewhat out of touch with the current discussion. > Using ZFC an injection is constructed from an uncountable set of > irrationals to a subset of the rationals. I haven't seen any such injection. All I've seen is a 1-1 mapping (injection) from irrationals to open intervals, where the intervals overlap to an extreme degree (uncountably many intervals have a point in common some/most/all of the time), and a mapping from those intervals to rational numbers within them, with uncountably many duplicate intervals for each rational due to those intervals overlapping so drastically. If you know of any injection of the type you cite, please summarize the argument for it. For example, if you can provide a demonstration of a mapping from irrationals to open intervals containing the irrationals such that no two intervals overlap, that would be truly amazing, because I believe it's impossible. (Counter-proof: Let i2 be an irrational, and let (i1,i3) be an open interval, where i1 The uncountably many pairs of distinct irrational numbers are > generated in a particular way thus that the open intervals (each > containing infinitely many rationals) connecting them are disjoint. If you're claiming an uncountably-infinite set of disjoint open intervals within the reals, I don't believe that's possible. > ... well-ordering the rationals ... Isn't that trivial, just use Cantor's zigzag mapping to the integers? > The physical universe, as an infinite collection of items, No such fact is in evidence. The total number of items in the physical universe might be finite for all we know. The total number of items in the *observable* universe almost surely is finite. > mathematically is its own powerset, You're a complete idiot!! Items, and sets of items, aren't the same thing at all. Regardless of whether the number of items in the Universe is finite or infinite, the number of subsets is two to that power, which is more than the number of individual items. > Ross You wouldn't even make a decent intern, IMO. === Subject: Solution Manual for Investment Analysis and Portfolio Management 7 or 8 edition needed (reilly/brown) I need this urgently. please contact me via alexlewyl@gmail.com please quote price and mode of payment === Subject: size of indexing set in repeated logical operations Let / represent logical or (inclusive or), / represent logical and, and - represent logical not. Let I be an indexing set. We can prove by induction that -( /_{n in I} x_n ) = /_{n in I} (-x_n) (DeMorgan's law) -( /_{n in I} x_n ) = /_{n in I} (-x_n) (DeMorgan's law) ( /_{n in I} x_n ) / y = /_{n in I} (x_n / y) (distributive) ( /_{n in I} x_n ) / y = /_{n in I} (x_n / y) (distributive) My question is, how large can the indexing set I be? Apparently since we can use mathematical induction to prove the above, then I can be countable infinite. But can the set I also be uncountably infinite? Good references that address this question would be especially appreciated. Dan Greenhoe === Subject: Re: size of indexing set in repeated logical operations > Let > / represent logical or (inclusive or), > / represent logical and, and > - represent logical not. Let I be an indexing set. We can prove by induction that -( /_{n in I} x_n ) = /_{n in I} (-x_n) (DeMorgan's law) > -( /_{n in I} x_n ) = /_{n in I} (-x_n) (DeMorgan's law) > ( /_{n in I} x_n ) / y = /_{n in I} (x_n / y) (distributive) > ( /_{n in I} x_n ) / y = /_{n in I} (x_n / y) (distributive) My question is, how large can the indexing set I be? Apparently > since we can use mathematical induction to prove the above, then I can > be countable infinite. But can the set I also be uncountably infinite? Good references that address this question would be especially > appreciated. Dan Greenhoe > Algebras where infinite unions exist are special algebras. Sometimes called sigma algebras. For example if take the following sets: X subset N and X is finite cardinality. Then finite unions exist. For X and Y, there is a Z, so that X union Y = Z. And so on if we have a countable number of sets. But infinite unions do not exists. Take for example Xi = {0, .., i}. Then sup Xi does not exists in the sets. Because sup Xi = {0, ...} which has not finite cardinality. So countable infinite unions CANNOT be proven to exist by induction per se! You can only show by induction that a finite union exists based on a binary operator. What concerns uncountable infinite unions, you should look at set theory. There is an axiom that sup S exists for every S, where we have: sup S = {x | exists y in S and x in y} This S can be uncountable. === Subject: Re: size of indexing set in repeated logical operations > Let > / represent logical or (inclusive or), > / represent logical and, and > - represent logical not. Let I be an indexing set. We can prove by induction that -( /_{n in I} x_n ) = /_{n in I} (-x_n) (DeMorgan's law) > -( /_{n in I} x_n ) = /_{n in I} (-x_n) (DeMorgan's law) > ( /_{n in I} x_n ) / y = /_{n in I} (x_n / y) (distributive) > ( /_{n in I} x_n ) / y = /_{n in I} (x_n / y) (distributive) My question is, how large can the indexing set I be? Apparently > since we can use mathematical induction to prove the above, then I can > be countable infinite. But can the set I also be uncountably infinite? > No. All that induction can prove is n is any finite number. If x_n, y are sets, you can prove your statements for any size of I and I doesn't have to be ordered. For statements x_n, y, you can't have infinitely long statements nor infinitely long conjections nor disjuctions. In which case n must be finite. Logic with infinitely long statements is a logic unto itself. ---- === Subject: Launching of Publications Online The Publications Online Board is proud to open its new Revue Publications Online to the scientific community. This journal is available to rapidly publish scentific papers, on the basis of the scientific commons license. A new Collaborative reviewing process is the main characteristic of this revue. More information is available on our website http://www.pub-online.org The Publications Online Board http://pub-online.org publisher@pub-online.org === Subject: soln manual- MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang I'm interesting in getting the complete solution manual for MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang. Let me know how to get file and make payment method. === Subject: Re: New list and email of contat for solutions manual http://www.ebookee.com/Digital-Systems-Principles-and-Applications-10th-Edit ion-_132783.html === Subject: Re: 1+x+x^(3^n) > from tommy's lost notebook or was it my old math book about fermat, on the last page , with no more space for the proof. ;-) anyways for non-negative integer n 1+x+x^(3^n) does not factor in polynomials over the > ring of integers. 1+x+x^(3^n) is polynomicly prime 1+x+x^(3^n) does not factor in integer polynomials. (the above 3 statements are equivalent.) tommy1729 > x =[x] tommy1729 well ... where are the experts now ? === Subject: Re: request for analytic continuation > plz give examples of analyticly continued functions > of a function A(z) that make their continuation in > this way : A(z) is defined as an infinite product of f(n) run > over the positive integers N. one of the continuations is then infinite product of [f(n)+g(n)] f(n) and g(n) must be constructed with standard > functions. tommy1729 well , where are the experts in analytic continuation now ? david C Ullrich ? === Subject: Re: a simple concept FACTORING question 1001 > all functions used are polynomials with rational > coefficients and positive integer valued for all > positive integer imput. (N0 -> N0) all variables are positive integers. g(x) is not a factor of f(x) > (factor in the sense of polynomial factors like > (x+1)(x-1)) but for every x > A, there exists a g(y) that is a > factor of f(x). > (weak version of the idea) in fact all factors of f(x) are of the type g(y). > (stronger version of the idea) an example with g(y) = 10y + 1 has already been given > by me before. see factoring tricks where a degree 4 polynomial > has been given that has as primefactors exclusively > primes 1 mod 10. > thereby satisfying the stronger version (and the > weaker too of course) now the question becomes (weaker) > 1) a) does there exist a g(y) = y^2 + 1 and an f(x) such > that the weaker idea holds ? b) does such a g(y) of irred degree 2 exist at all ? c) does such an irred g(y) > degree 1 exist at all ? > (stronger) 2) assuming it is already proved that g(y) and f(x) both > generate an infinite amount of primes; a) does there exist a g(y) = y^2 + 1 and an f(x) such > that the stronger idea holds ? b) does such a g(y) of irred degree 2 exist at all ? c) does such an irred g(y) > degree 1 exist at all ? tommy1729 such a simple question ... no answers ? === Subject: Re: optimized geometry > let A be a set of positive real values with finite > elements, and min 5 elements. let the real elements denote the edges of a closed > non-intersecting polygon. what is the maximum area of this polygon in terms of > the elements ? T[A] = max area for A. tommy1729 surely an expert like david C Ullrich can solve such a simple question ... tommy1729 ps : hahaha === Subject: Re: optimized geometry > let A be a set of positive real values with finite > elements, and min 5 elements. let the real elements denote the edges of a closed > non-intersecting polygon. what is the maximum area of this polygon in terms of > the elements ? T[A] = max area for A. tommy1729 surely an expert like david C Ullrich can solve such a simple question ... tommy1729 ps : hahaha ** Have you ever stopped to think (figure of speech) for a moment that your questions may be uninteresting for other people to reply? Perhaps your questions, or some of them, are so nonsensical or ill- posed sometimes that people won't even take the work to look into them seriously? You also patronize and mock others when you write so simply a question...then why don't you answer yourself for yourself's sake? Remember: not all questions have (so far, at least) answer, leave alone if questions are stupid or ill-posed, which may be your case. Tonio Pd. You seemingly hysterical hahaha ' s don't seem to be very helpful to make your question appear more interesting... === Subject: Re: Continuous functions between topological spaces On Oct 1, 10:27 am, Jose Capco Let's say I have a continuous map f : X --> Y between top. spaces X >and Y. > If for any open subset U of X, there is an open set V such that f(U) >contains V (I don't suppose that then this map becomes open, does >it?) .. is there a name for such a function? No. > Continuous. > For all open U subset X, open nulset subset f(U). Of course I was assuming a nontrivial case when V is nonempty. For those who are still following this thread.. I have posted a related thread: in which these functions are more discussed.. I am investigating these functions a little more before I call it quits :) Jose Capco === Subject: uniform distribution on the unit sphere hello, i'm about to read a book about inner point algorithms, and repeatedly there is the following argument: let lambda be standard gaussian, lambda in R^n then is lambda / norm{lambda} uniformly distributed on the unit sphere in R^n i can't really see why this is the case and i haven't been able to find any reference. i hope someone could give me a hint or a referene cheers === Subject: Re: uniform distribution on the unit sphere > hello, i'm about to read a book about inner point algorithms, and repeatedly > there is the following argument: > let lambda be standard gaussian, lambda in R^n > then is > lambda / norm{lambda} uniformly distributed on the unit sphere in > R^n i can't really see why this is the case and i haven't been able to > find any reference. > i hope someone could give me a hint or a referene cheers Because the pdf of the standard Gaussian in R^n depends only on the distance from the origin. === Subject: Re: uniform distribution on the unit sphere hello, i'm about to read a book about inner point algorithms, and repeatedly > there is the following argument: > let lambda be standard gaussian, lambda in R^n > then is > lambda / norm{lambda} uniformly distributed on the unit sphere in > R^n i can't really see why this is the case and i haven't been able to > find any reference. > i hope someone could give me a hint or a referene cheers It's isotropic (no direction preference), and then simply normalized to have the same direction (still isotropic) with length 1. It's a property of gaussian; multivariate uniform would prefer corner directions, for instance. -- rhhardin@mindspring.com On the internet, nobody knows you're a jerk. === Subject: =?iso-8859-1?q?G=F6del_book_(first_chapter_online)?= I have put the short, accessible, first chapter of my book on G.9adel's Theorems (CUP, 2007) on line. Go to http://www.godelbook.net to download. Peter Smith logicmatters.blogspot.com === === === Subject: request hi i need Basic Engineering Circuit Analysis 8th irwin solution and problem solving. please help me. === Subject: Euclid in Russian online? I need to obtain a copy of Euclid's elements translated into Russian, preferably in a form that can be downloaded. If I could obtain a copy translated into Georgian (Kartuli) that would also be good. I would be grateful for any assistance. Lancelot Fletcher writing from Tbilisi === Subject: Re: Alien math. (was Re: Another example of Schuh as moron (was Another Synthol moron)) Analiencognition indeed might not perceive things the same way. It's almost guaranteed not to, I'd say, unless their brains just happen to be wired up like ours! In which case, they wouldn't be so alien, would they.... > But that doesn't mean that what we perceive in our mathematics is > wrong on their planet. It just means they would see, and work with, > a different part of the truth than we do. Indeed, I never said our math was wrong -- just works for us, given the way our brains are. Since math is but a very specialized kind of language, it's entirely plausible that alien sensibilities arising from alien brain structures can only result in an alien language, an alien symbolic system, an alien way of representing the world to themselves and manipulating those representations in useful ways.... > One book onmathnoted that some aliens might be satisfied with > demonstrating that what we call Riemann's conjecture works out pretty > far by computer searches, and not be concerned with exact mathematical > proofs as we are - as an example of howalienmathcould be different. Well, this subject header, alien math, is misleading WRT my thesis, insofar as my thesis is that aliens might well not have a mathematics at all -- not just a different one or more advanced one compared to ours, but nothing we'd call mathematics by any stretch of the imagination. And I cite as proof the fact that a telepathic species would not have a need for language...therefore it would not have language...math, being a specialized kind of language, would also not exist for them.... > The history of mathematics shows how there can be differences in > mathematics - analienrace could use quaternions instead of vector > mechanics; they could use a notation for derivatives that doesn't > normally specify with respect to what they are derivatives. Perhaps they could be vaguely like human mystics who perceive the reality behind our symbols, linguistic and, more specifically, mathematic; and thus perceiving reality itself, as opposed to by way of intellectual vehicles like math or language, they would not need such vehicles, and having never needed such things, would have never had them. Thus, these aliens would not have math. > Differences in base notation are trivial but obvious - we could even > as the first several terms of their continued fraction expressions. And the unusual ancient Egyptian notation for fractions can be noted. Yes, but you see, I'm talking about something much more radical than simply a different or more advanced mathematics. I'm basically asking the question, Does God need math? Seriously...if God were just some super-intelligent alien like in many a science fiction tale, well, would he need math? Did God create the earth, the universe, by first doing all his sums and double-checking them?? > Ultimately, though, aliens live in the same physical universe as we > do, and some of the same basic rules of logic and arithmetic are > likely going to be pretty hard for them to avoid. But don't you see that those rules of logic and arithmetic are based on our human brains, our human capacities...it's like how a computer and a grandmaster can both play chess, but they do so differently, obviously...likewise, an artist and a computer ray-tracing program...before a computer ever figured out vector graphics, human beings were doing foreshadowing (even before the geometric revolution in Renaissance painting)...similarly, an alien cognition could very well not need such a contrivance, such a crutch, as mathematics...not only would they not need it, given some other supernatural-seeming faculty of their evolutionary development, but they would never even have come across it, in all likelihood.... > Soalienmathis > more likely to be something we can learn from than something that will > be eternally incomprehensible. Well, this would be a good point of departure for a Hugo-winning novel, methinks! > John Savard === Subject: Re: solutions manual >I have the following solutions manuals in pdf. If you need any of them, send me email at abole...@yahoo.com > I accept paypal payments only >* Solutions manual for Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer > * Solutions manual for Analytical Mechanics, 7th Edition, by Fowels, Cassiday > * Solutions manual for An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin > * Solutions manual for An Introduction to the Mathematics of Financial Derivatives, 2nd Ed.,by Neftci [ISBN:0125153929] > * Solutions manual for Antenna Theory, 2nd Ed., by Balanis > * Solutions manual for Antennas for all Applications, 3rd Edition, Kraus, Marhefka > * Solutions manual for Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) > * Solutions manual for Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley > * Solutions manual for Applied Numerical Methods with MATLAB for Engineers and Scientists,1st Ed,. by Chapra > * Solutions manual for Applied Statistics and Probability for Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) > * Solutions manual for Applied Strength of Materials, 4th Edition, by Mott > * Solutions manual for A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen,Andre > * Solutions manual for Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi > * Solutions manual for A Course in Game Theory by Osborne, Rubinstein > * Solutions manual for A Course in Algebraic Number Theory by Cohen > * Solutions manual for Adaptive Filter Theory, 4th Edition, by Haykin > * Solutions manual for Adaptive Control, 2nd. Ed., by Astrom, Wittenmark > * Solutions manual for Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) > * Solutions manual for Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) > * Solutions manual for Advanced Macroeconomics, 1st Ed., by David Romer > * Solutions manual for Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] > * Solutions manual for Advanced Modern Engineering Mathematics, 3rd Ed., by G. James > * Solutions manual for A First Course In Differential Equations, 7th Edition, by Zill, Cullen > * Solutions manual for Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text ebook and solution manual) > * Solutions manual for Basic Business Statistics: Concepts and Applications, 10th Ed., by > Berenson, Krehbiel, Levine (chap1-18) > * Solutions manual for Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin > * Solutions manual for Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) > * Solutions manual for Bioprocess Engineering Principles by Doran > * Solutions manual for Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson,Hostetler, Edwards > * Solutions manual for Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler > * Solutions manual for Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker > * Solutions manual for College Physics, Volume 1: 7th Edition, by Serway, Faugh > * Solutions manual for College Physics, Volume 2: 7th Edition, by Serway, Faughn > * Solutions manual for Communications Systems, 4th Ed., by Haykin > * Solutions manual for Communications Systems Engineering, 2nd Edition, by Proakis > * Solutions manual for Computational Techniques for Fluid Dynamics by Srinivas, Fletcher > * Solutions manual for Computer Networks, 4th Ed., by Andrew S. Tanenbaum > * Solutions manual for Computer Networks: A Systems Approach, 3rd Edition, by Davie > * Solutions manual for Control Systems Engineering, 4th Ed., by Norman Nise > * Solutions manual for Corporate Finance, 6th Edition, by Ross > * Solutions manual for C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto > * Solutions manual for Calculus Early Transcendental, 5th Ed., by James Stewart > * Solutions manual for Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis > * Solutions manual for Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney,Demana, Kennedy > * Solutions manual for Calculus: Multivariable, 5th Edition, by James Stewart > * Solutions manual for Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart > * Solutions manual for Calculus, Single and Multivariable, 3rd Ed., by Hughes-Hallett,McCallum > * Solutions manual for Device Electronics for * Solutions manual for Integrated Circuits 3rd Edition by Muller > * Solutions manual for Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold > * Solutions manual for Digital And Analog Communication Systems 7th Ed., Leon W. Couch > * Solutions manual for Digital Communications, 4th Edition, by Proakis > * Solutions manual for Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar > * Solutions manual for Digital Design, 4th Edition, by Mano, Ciletti > * Solutions manual for Digital Image Processing, 2nd Edition, by Gonzalez, Woods > * Solutions manual for Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY for Chapters 3, 5, 6, 10) > * Solutions manual for Digital Signal Processing: A Computer Based Approach, 1st Ed., by Mitra > * Solutions manual for Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S.Mitra > * Solutions manual for Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S.Mitra > * Solutions manual for Digital Signal Processing: Principles, Algorithms and Applications,3rd Edition, by Proakis > * Solutions manual for Discrete Time Signal Processing, 2nd Edition, Oppenheim > * Solutions manual for Dynamics of Mechanical Systems by C.T.F. Ross > * Solutions manual for Data and Computer Communications, 8th Edition by Stallings > * Solutions manual for Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol.for Chapters 2-21, odd only) > * Solutions manual for Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi Design of Analysis of Experiments, 6th Edition, Montgomery (missing > chapter 6-8) > * Solutions manual for Design of Machinery, 3rd Ed by Robert L. Norton > * Solutions manual for Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., by Sergio Franco > * Solutions manual for Design With Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., by Sergio Franco > * Solutions manual for Elementary Principles of Chemical Processes, 3rd Ed., by Felder,Rousseau > * Solutions manual for Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler > * Solutions manual for Engineering and Chemical Thermodynamics, by Koretsky [ISBN:0471385867] (No sol. for chapt 6) > * Solutions manual for Engineering Circuit Analysis, 6th Edition, Hyat > * Solutions manual for Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck > * Solutions manual for Engineering Electromagnetics, 7th Ed., Hayt, Buck > * Solutions manual for Engineering Fluids Mechanics 7th Edition by Crowe > * Solutions manual for Engineering Fluids Mechanics 8th Edition by Crowe > * Solutions manual for Engineering Mathematics, 4th Ed., by John Bird > * Solutions manual for Engineer Mechanics: Dynamics, 4th Ed., by Bedford > * Solutions manual for Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler > * Solutions manual for Engineering Mechanics: Dynamics 11th Ed. by Hibbeler > * Solutions manual for Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige > * Solutions manual for Engineering Mechanics: Statics, 4th Edition - A. Bedford, Wallace Fowler > * Solutions manual for Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige > * Solutions manual for Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige > * Solutions manual for Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler > * Solutions manual for Engineering Mechanics: Statics 11th Ed. by Hibbeler > * Solutions manual for Experiments with Economic Principles by Bergstrom, Miller > * Solutions manual for Econometric Analysis, 5th Edition, by Greene > * Solutions manual for Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira > * Solutions manual for Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar > * Solutions manual for Electric Circuits 6th Ed. by Nilsson > * Solutions manual for Electric Circuits 7th Ed. by Nilsson > * Solutions manual for Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans > * Solutions manual for Electric Machinery Fundamentals, 4th Ed by Chapman > * Solutions manual for Electromagnetic Fields and Waves by Iskander > * Solutions manual for Electronic Circuit Analysis, 2nd Ed., by Donald Neamen > * Solutions manual for Electronics, 2nd Ed., by Allan R. Hambley > * Solutions manual for Elementary Differential Equations, 8th Edition, by Boyce, DiPrima(some odd/even) > * Solutions manual for Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition,by Ulaby > * Solutions manual for Fundamentals of Digital Logic with Verilog Design, 1st Edition, by Brown, Vranesic > * Solutions manual for Fundamentals of Electric Circuits, 2nd Edition, by Alexander > * Solutions manual for Fundamentals of Electromagnetics with Engineering Appls by Wentworth > * Solutions manual for Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. > * Solutions manual for Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... > * Solutions manual for Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... > * Solutions manual for Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... > * Solutions manual for Fundamentals of Logic Design, 5th Ed., by Roth Jr. > * Solutions manual for Fundamentals of Machine Component Design, 3rd Ed., by Juvinall > * Solutions manual for Fundamentals of Machine Component Design, 4th Ed., by Juvinall >read more E... >Can you please email me, * Solutions manual for Engineering Circuit > Analysis, 6th Edition, Hyat to > skida2...@msn.com > Hi there, >I need Solutions manual for Computer Networks, 4th Ed., by Andrew S. >Tanenbaum >could you please send one and procedure to get it...? >I need solutions manual for Design of Analog CMOS Integrated Circuits >by Razavi..Could you please let me know how I can go about getting >it.. > Karthik > If you could, please send Solutions manual for Engineering Mechanics: > Statics, 6th Ed., Meriam, Kraige to this gmail if you are able to see > it, or uga06@hotmail.com. bujiie >hi, > iam unaable to se ur email id can u mail me the manual for Solutions manual for Analysis and >Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer at my email id please > my email id is m.shamkrishna@gmail.com >thank >shyamak I was needing the Solution manual for the sixth edition engineering mechanics statics meriam and kraige, if any one could send this to jessiepooluvsyou@gmail.com === Subject: Re: request for help with parabolic leaf calculation, is this the right newsgroup? > ...is this the right newsgroup for me to post this in? > Probably not. sci.math would be my first suggestion. (I've cross- > posted this reply to sci.math, so you don't have to post there again.) > --- Christopher Heckman The mathematical computation of the profile is an easy task.You may > need more engineering fabrication guidance. By approximating curved surfaces with flat metal tin sheets,bending > and using it as a reflector, some loss of electrical gain would occur. > It is better to make an inexpensive brick mold using a sweeping > template,choose fiberglass cloth and thermoset resin and deposit metal > or metal paint for RF reflections on the inner surface. Narasimham One application for this will be making solar cookers as easily and inexpensively as possible, a guy who's traveling to Keyna wants to start building simple kits there, possibly with cardboard and some sort of foil. I have no idea how reflective the foil will be at this time. Mike === Subject: Varberg Calculus Manual Looking for a comprehensive solutions manual for: Calculus with Analytic Geometry by Varberg, Purcell, Rigdon-Prentice Hall 8th or 9th ed. Not looking for the student solutions manual. Need to solve a eeven numbered problem from the text. Need ASAP. === Subject: Question in Galois group of a polynomial! Hi! In exercising algebra with Hungurford text, one problem does not seem to be easily solved and so I decide to share this problem with you. The problem is, Show that there is no transitive subgroup of order 6 in S_4 This is contained in the chapter of Galois theory, more precisely, Galois group of polynomial. In that chapter, there is a theorem as follows If f is a degree n irreducible separable polynomial over K and F is a splitting field over K of f. Let G be the galois group of f, that is, Aut_K ^ F. Then, F is galois over K and n divides the order of the galois group. Furthermore this group is isomorphic to the transitive subgroup of S_n. I think this problem is intended to use this theorem. More precisely, assume the existence of such subgroup of S_4 and then there are two fields K, F s.t.G is isomorphic to Aut_K ^ F.(This is well known theorem.) If we can show there is irreducible polynomial f over K which makes F the splitting field over K of f, then by the above theorem 4 should divides 6 and so we get the contradiction. But this is my barrier to proceed. So I hope any one have some bright in this point and share the idea with me. I know there is straightforward solution for this that has nothing to do with this chapter's content. That is, use the fact that there is exactly 2 groups of order 6 and they are Z_6 and S_3. Both cannot be a transitive subgp and so we can solve this problem. But this is not desired one to me and I think this is against with author's intention. === Subject: 25 Cc: ghgh 2YXZgtin2LfYuQo= === Subject: Re: 25 T24gT2N0IDEyLCAxMTozNSBhbSwg2KfZhNiv2YjYs9ix2YogPGRvc3MuLi5AaG90bWFpbC5jb20+ IHdyb3RlOgo+INmF2YLYp9i32LkKCgo0Mi4K === Subject: Equation g(y,x) +g(2x,y)+g(x,x)=g(2y,x+1)+g(4x,y+1)+g(2x,x+1) g (x,y) is defined all y in R , x > 2 . g is x and y derivable . g verified the following equation : g(y,x) + g(2x,y)+ g(x,x) = g(2y,x+1)+ g(4x,y+1)+ g(2x,x+1) (1), Is there any method to simplify and give solutions to (1) Alain === Subject: Special properties of the ring of complex numbers Originator: israel@math.ubc.ca (Robert Israel) I am wondering whether the ring of complex numbers (or the algebraic numbers) has any special place among all rings (let's just restrict to rings with at most continuum cardinality.) For example, the ring of integers has precisely one homomorphism to any ring; this is the sort of special property that I have in mind. Of course, any special property of the complex numbers will presumably be much more sophisticated. For those who know some category theory, I am essentially asking the following: does the ring of complex numbers have any special properties, which would allow us to identify it (up to isomorphism) in the category of all rings and ring homomorphisms? We can spot the ring of integers up to isomorphism in this way, since it is an initial object in the category. If there is nothing special to say for the complex or algebraic numbers, are there any other rings, aside from the integers, which do have special properties along these lines? Looking forward to your thoughts, Jamie Vicary. === Subject: Re: Special properties of the ring of complex numbers I am wondering whether the ring of complex numbers (or the > algebraic numbers) has any special place among all rings (let's just > restrict to rings with at most continuum cardinality.) For example, > the ring of integers has precisely one homomorphism to any ring; this > is the sort of special property that I have in mind. Of course, any > special property of the complex numbers will presumably be much more > sophisticated. For those who know some category theory, I am essentially asking > the following: does the ring of complex numbers have any special > properties, which would allow us to identify it (up to isomorphism) in > the category of all rings and ring homomorphisms? We can spot the ring > of integers up to isomorphism in this way, since it is an initial > object in the category. If there is nothing special to say for the complex or algebraic > numbers, are there any other rings, aside from the integers, which do > have special properties along these lines? Looking forward to your thoughts, > Jamie Vicary. you can characterize IR as a complete ordered field (not sure for the English expresssion for vollstaendig angeordnet), then IC is the algebraic closure (or even as K(sqrt(-1)) or similar, all are equivalent once you have the Reals). === Subject: Unsolvable polynomial with real roots only Originator: israel@math.ubc.ca (Robert Israel) Hi all, Does anyone knows an example of an unsolvable polynomial of odd degree that have *only real* roots? To be precise: I'm searching for a polynomial f such that: 1) f has rational coefficients and 2) f has odd degree and 3) f has only real roots and 4) the roots of f cannot be expresed in terms of radicals. Przemek P.S. The classical examples do not work: t^5-t-1 ==> only one real root and two pairs of conjugated nonreal t^5-10t+2 ==> three real roots and two conjugated nonreal === === === Subject: log concave function hello all, is the sum of two log-concave functions log-concave? === Subject: On Sara's method of eating dove bars Recently, Sara has become enamored of the vanilla ice cream with dark chocolate Dove bar miniatures . Unfortunately, the stores in our area tend to not stock the vanilla only boxes, but to stock the mixed vanilla and chocolate bars. The chocolate dove bars being deemed definitely inferior, the following dessert protocol has been established: First, Sara selects a dove bar at random from those remaining in the box. If it is either vanilla or it is the last bar in the box, she will eat it and thus conclude the dining portion of our evening. If it is neither the last bar or vanilla, she will invite me to select a bar at random from the box. If I select a vanilla bar I will offer to exchange it with hers (gallant soul that I am) and we will eat them, again concluding the dessert portion of our evening. I have no particular attraction or aversion to Dove bars, but I like interesting problems, and I was interested in figuring out how many of the Dove bars I end up eating. If the box was infinite, and contained half vanilla and half chocolate, then I'd expect to eat about 1/3 of the bars, or 2/3 of the chocolate ones, since I expect to eat 1/2 a bar per day and Sara expects to eat 1 bar per day, and I eat only chocolate ones. Unfortunately, we lack the freezer space to keep an infinite box of Dove bars, and only have packs of 16 (which I assume are 8 vanilla and 8 chocolate). A quick computation tells me that I will eat 33356/6435 Dove bars per pack, which is slightly less that 16/3. This is sort of what I would expect because about 1/3 of the time the last dessert for a box begins with only one chocolate bar in the box, and I am relieved of my ice cream consumption responsibilities. What puzzles me is that if I consider the number of dove bars that I eat given that I start with a box containing n vanilla and n chocolate bars, I appear to end up eating 2 n/3 + 4/27 + O( 1/n ) bars. I can come up with no clear explanation for the 4/27. Note: I've computed enough digits to be quite sure that it is 4/27, but I cannot prove that either. Mathematica does not seem to help either, though I would think that the fact the the function is a sum of trinomial coefficient would make it amenable to the Wilf-Zeilberger algorithm. The number of bars I expect to eat given a box of 2n bars with n vanilla and n chocolate is c(n)= ( sum(k = [(n+1)/2] to n | k * comb( 2n - k, k) * comb( k, n - k))+ sum(k = [n/2] to n | k * comb( 2n - k - 1, k) * comb( k, n - k - 1)))/comb( 2n, n) where [x] is the floor function and comb is the binomial function. === Subject: Continuity-Need help. f(x)= x^1/3 if x is rational, and 0 if x is irrational I know that this function is continuous at x=0 but I am not sure how to prove it, using .83A and .83A. === Subject: Re: Continuity-Need help. > f(x)= x^1/3 if x is rational, and 0 if x is irrational I know that this function is continuous at x=0 but I am > not sure how to prove it, using [epsilon] and [delta]. Can you write an epsilon-delta proof for the continuity of x^(1/3) at x=0? If so, then hardly any changes will be needed for what you want, since the values of your function are the same or better for what you need. Dave L. Renfro === Subject: Re: Continuity-Need help. > f(x)= x^1/3 if x is rational, and 0 if x is irrational I know that this function is continuous at x=0 but I am > not sure how to prove it, using [epsilon] and [delta]. Can you write an epsilon-delta proof for the continuity > of x^(1/3) at x=0? If so, then hardly any changes will > be needed for what you want, since the values of your > function are the same or better for what you need. Dave L. Renfro no =(, I'm rather new at using [epsilon] and [delta]. All I have is few notes we did in class, not quite sure how to start it. === Subject: How to integrate this I would integrate this: R= -INTEG[0, z0] { rdn/dr / (n + rdn/dr) dz} with the Simpson's method, but I don't understand the notation (rdn/dr is a bit confusing). That is the integral (3) taken here: http://www.journals.uchicago.edu/PASP/journal/issues/v110n748/980027/980027. web.pdf Please, could somebody help me? Cristiano === Subject: solutions I need the solutions manual to Digital and Analog Communication Systems 7th edition Leon Couch === Subject: Re: Complete Electronic (.pdf/doc) Solution Manuals. Get witihn 30 Minutes! >On Sep 17, 7:02 am, karthik Balaji- chennai romba hot machi!! > I have the comprehensive solution manual, solutions manual, solutions > manuals, in electronic format for the following textbooks. They > include complete solutions to all the problems in the text, except > where noted below in the listing. Payment is through Paypal. Email me > bookstoday777[at]gmail.com but please DO NOT POST HERE because I will > not be able to help you, but instead email and ask me for the solution > that you need. Downloads emailed immediately - within 30 minutes! >A Course in Game Theory by Osborne, Rubinstein > A Course in Algebraic Number Theory by Cohen > Adaptive Filter Theory, 4th Edition, by Haykin > Adaptive Control, 2nd. 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James > A First Course In Differential Equations, 7th Edition, by Zill, Cullen > Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text > ebook and solution manual) > Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray, > Hurst, Lewis, Meyer > Analytical Mechanics, 7th Edition, by Fowels, Cassiday > An Interactive Introduction to Mathematical Analysis, by Jonathan > Lewin > An Introduction to the Mathematics of Financial Derivatives, 2nd Ed., > by Neftci [ISBN: 0125153929] > Antenna Theory, 2nd Ed., by Balanis > Antennas for all Applications, 3rd Edition, Kraus, Marhefka > Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) > Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley > Applied Numerical Methods with MATLAB for Engineers and Scientists, > 1st Ed,. by Chapra > Applied Statistics and Probability for Engineers, 3rd Ed., by > Montgomery, Runger (Selected Solutions) > Applied Strength of Materials, 4th Edition, by Mott > A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen, > Andre > Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi >Basic Business Statistics: Concepts and Applications, 10th Ed., by > Berenson, Krehbiel, Levine (chap1-18) > Basic Engineering Circuit Analysis, 7th Ed., by J. 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Sandler > Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson, > Backhurst, Harker > Thornton > College Physics, Volume 1: 7th Edition, by Serway, Faugh > College Physics, Volume 2: 7th Edition, by Serway, Faughn > Communications Systems, 4th Ed., by Haykin > Communications Systems Engineering, 2nd Edition, by Proakis > Computational Techniques for Fluid Dynamics by Srinivas, Fletcher > Computer Networks, 4th Ed., by Andrew S. 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Scott Fogler > Engineering and Chemical Thermodynamics, by Koretsky [ISBN: > 0471385867] (No sol. for chapt 6) > Engineering Circuit Analysis, 6th Edition, Hyat > Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck > Engineering Electromagnetics, 7th Ed., Hayt, Buck > Engineering Fluids Mechanics 7th Edition by Crowe > Engineering Fluids Mechanics 8th Edition by Crowe > Engineering Mathematics, 4th Ed., by John Bird > Engineer Mechanics: Dynamics, 4th Ed., by Bedford > Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler > Engineering Mechanics: Dynamics 11th Ed. by Hibbeler > Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige > Engineering Mechanics: Statics, 4th Edition - A. Bedford, Wallace > Fowler > Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige > Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige > Engineering Mechanics: Statics, 10th Ed., by Russell C. 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Anderson, Jr. > Fundamentals of Applied Electromagnetics, 1st Ed., 2001 Media Edition, > by Ulaby > Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition, > by Ulaby > Fundamentals of Digital Logic with Verilog Design, 1st Edition, by > Brown, Vranesic > Fundamentals of Electric Circuits, 2nd Edition, by Alexander > Fundamentals of Electromagnetics with Engineering Appls by Wentworth > Fundamentals of Fluid Mechanics, 5th Ed. by- Hide quoted text - - Show quoted text -... read more E I need the solutions manual to Digital and Analog Communication Systems 7th edition leon couch mtr08004 at gmail dot com === Subject: Re: Complete Electronic (.pdf/doc) Solution Manuals. Get witihn 30 Minutes! I need the solution manual for, Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton, as soon as possible, because I have an exam on Friday, 12 Oct.. Whoever has it, please send me an e-mail with the price and a sample page, because I already sent e-mails to people who say they had it, but nobody has replied. e-mail to: sunsad79 (at)yahoo.com === Subject: deep holes of the Leech lattice I read about the Leech lattice on http://en.wikipedia.org/wiki/Leech_lattice Is there a description of the coordinates of the deep holes at --- J K Haugland http://home.no.net/zamunda === Subject: Re: deep holes of the Leech lattice > I read about the Leech lattice on http://en.wikipedia.org/wiki/Leech_lattice Is there a description of the coordinates of the deep holes at there are two classic papers on this by conway, sloane, and parker the covering radius of the leech lattice and twenty-three constructions for the leech lattice that build the description of these deepest holes there is a direct correspondence to niemeier lattices in dimension 24 here if you are looking for coordinate descriptions of these points see the section on dimension 24 at http://www.research.att.com/~njas/lattices/ -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: Students Leaving School Unprepared For College, Work Of 300 questions asked in presidential candidate debates this year, >number that addressed this issue: eight. Total Federal budget 2006 2.7 trillion. Dept of Education outlays 84 > billion. Sounds like the number of questions roughly match the > importance of education in the federal budget. And why should the rich pay to educate the children of the poor? Heck, kids should get jobs so they'll have health coverage, and they can pay for their own schooling with their wages at the same time. American kids are soft and flabby enough without your darn coddling. >These figures tell us that while America's high school system works >for some students, it fails many, if not most. The number of questions asked of presidential candidates tells us > nothing about this. Indeed, it suggests that the American people feel > no especial concern about education. Oh c'mon. What is important to know about presidential candidates is how much they spend on a haircut and how much cleavage they'll show. >America's high schools are at risk of becoming a disaster, No You mean they became disasters years ago? The magic of the marketplace says things will improve when kids start bundling campaign contributions. >yet few of our political leaders are talking about it. Presidential candidates shouldn't waste their time. State officials > do talk about it. What? No NCLB posturing? >That a million students drop out each year is terrible. >One million? that seems a bit low - if supposely 30% of the students are >dropping out - that would mean that there are only about 30+ million >students in public education. 48 million school kids over 13 grades means about 3.7 million 12th > graders. 1 million dropouts is around 27% of them. Assume essentially 0 dropouts in k-8 grade: abt 1 million dropouts > number of GED tests passed - until 2000, abt 700 million per year, > more recently around 550 million per year. 2005, percentage of 16-24 year olds not in school who have not > completed high school or GED: 9.4% > this percentage is the lowest percentage of the previous 35 years > 1970: 15% > 1980: 14% > 1990: 12% > 2000: 11% 2006: percentage of population 25-29 which had completed high school > or higher: 86.5%, essentially unchanged for 20 years, 11% higher than > in 1970 > The older the age group measured, the more that the numbers include > immigrants who had less than a high school education. In 2000, 48% of > Hispanics age 25 or older had not graduated high school. While school districts and states clearly have roles in this issue, so >do our national leaders. Education is not mentioned in the Federal constitution as a concern of > the Federal government. Education funding therefore tends to be > through the back door based on other factors that ARE covered by the > constitution. Therefore, no federal official clearly has a role. What about the Secretary of Education? --Jeff -- Every gun that is made, every warship launched, every rocket fired, signifies in the final sense a theft from those who hunger and are not fed, those who are cold and are not clothed. --Dwight Eisenhower === Subject: Re: Students Leaving School Unprepared For College, Work Of 300 questions asked in presidential candidate debates this year, >number that addressed this issue: eight. Total Federal budget 2006 2.7 trillion. Dept of Education outlays 84 > billion. Sounds like the number of questions roughly match the > importance of education in the federal budget. And why should the rich pay to educate the children of the poor? Because we the people decided that they should. If they don't like it, they can leave, or try to convince we the people otherwise (good luck). The justification for public education, of course, is that all of society benefits from universal education. >Heck, kids should get jobs so they'll have health coverage, and >they can pay for their own schooling with their wages at the >same time. What jobs that pay for health coverage do you think are available to American kids? >American kids are soft and flabby enough without your darn coddling. What coddling? We have had a national consensus for universal public education and for child labor laws for more than a century. Nothing has changed to make either of them unnecessary. >These figures tell us that while America's high school system works >for some students, it fails many, if not most. The number of questions asked of presidential candidates tells us > nothing about this. Indeed, it suggests that the American people feel > no especial concern about education. Oh c'mon. What is important to know about presidential >candidates is how much they spend on a haircut and how much >cleavage they'll show. I don't recall seeing those questions asked of candidates at debates. >America's high schools are at risk of becoming a disaster, No You mean they became disasters years ago? No. >The magic of the >marketplace says things will improve when kids start bundling >campaign contributions. They don't need to. >yet few of our political leaders are talking about it. Presidential candidates shouldn't waste their time. State officials > do talk about it. What? No NCLB posturing? NCLB is a bad joke piece of demagoguery. Presidents shouldn't waste their time. >While school districts and states clearly have roles in this issue, so >do our national leaders. Education is not mentioned in the Federal constitution as a concern of > the Federal government. Education funding therefore tends to be > through the back door based on other factors that ARE covered by the > constitution. Therefore, no federal official clearly has a role. What about the Secretary of Education? The Secretary of Education has no clear role in education, despite the title. lojbab === Subject: Re: Students Leaving School Unprepared For College, Work <13gptj8lljlt5c9@corp.supernews.com Of 300 questions asked in presidential candidate debates this year, >number that addressed this issue: eight. Total Federal budget 2006 2.7 trillion. Dept of Education outlays 84 > billion. Sounds like the number of questions roughly match the > importance of education in the federal budget. And why should the rich pay to educate the children of the poor? I don't know if this questions was intended to be sarcastic, but I will take it seriously and answer it thusly. Other than the fact that we are all part of the same society. It is in their own best interest to do so. An ounce of prevention is worth a pound of cure A result of failure to educate people is increased crime. It is better to pay a few bucks to educate someone than to pay for the results of crimes committed by people who have otherwise insufficient skills to support themselves. The same question might be asked about public funding for any human endeavor. Why should I pay for something if I don't use it? This question has been asked repeatedly and the answer is always the same. Indeed, rather than phrasing it as why should the rich pay, it might also be phrased as why should someone who does not/will not have children pay? We all pay COLLECTIVELY for the activities of ALL OF US. === Subject: Re: Students Leaving School Unprepared For College, Work >Of 300 questions asked in presidential candidate debates this year, >number that addressed this issue: eight. > Total Federal budget 2006 2.7 trillion. Dept of Education outlays 84 > billion. Sounds like the number of questions roughly match the > importance of education in the federal budget. > And why should the rich pay to educate the children of the poor? >I don't know if this questions was intended to be sarcastic, but I >will >take it seriously and answer it thusly. >Other than the fact that we are all part of the same society. >It is in their own best interest to do so. >An ounce of prevention is worth a pound of cure >A result of failure to educate people is increased crime. It is >better >to pay a few bucks to educate someone than to pay for the results >of crimes committed by people who have otherwise insufficient skills >to support themselves. But educate them. not put them through 12 years of what often amounts to nothing more than daytime imprisonment. Develop their brains to what they, as individuals, can do, instead of keeping all of the same age in gridlock until at least high school. Mental abilities vary quite dramatically, as I have found with my two children, both of whom went on to get PhD's. Also, in my many years of teaching, I have found huge differences in the students in classes, including graduate courses. We need people who can think to do the teaching, also, not those who have been indoctrinated to proceed by plans designed by those who do not know their subjects. If we proceed to have a strong high school curriculum, we will find that quite a few cannot complete it. Teach them what they can learn at the rate they can learn it, and augment it with training. For the rest, teach it at the rate they can manage it, with possibly 15 years for the slow one, to possibly 6 for the gifted. If it is not desired for them to leave that early, teach them first class honors college material, so they get an early college degree, and maybe even a PhD at 17 or 18. -- 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: Students Leaving School Unprepared For College, Work a baby - and then go back after several years and get her GED and > successfully get through a 2 year college nursing program, all while > working a full time job and doing the day-to-day wife/family stuff. My > guess is my sister never used a microscope before college. One word: MOTIVATION. Your sister seems to have had some. She does merit some kudos for persistence and diligence. I would say well done to your sister except for one thing. I think it is irresponsible to have a baby before one gets sufficiently educated to support yourself and the baby. In fact, I think we should pass laws requiring a LICENCE before having a baby. To obtain that license one should have to produce concrete evidence that you are capable of supporting and caring for a baby. Of course this is an unrealistic expectation and totally unenforceable. [what would the punishment be? Jail? Taking the baby away? Either one dumps the problem of raising the child on the rest of society. I vaguely recall a science fiction short story in which licences were required. If you had an unlicenced baby you would have to defend your actions with your life. A volunteer would be selected from the public who would engage in mortal combat with the one who had the unlicensed baby. The objective there was more toward ZPG, but the idea was interesting; an unlicensed baby is born, someone dies == zero sum] An interesting idea ala J. Swift: How about if we make failure to be responsible a crime? examples of failure to be responsible would be: failing to educate oneself, having a baby one can't adequately support, drinking/doing drugs while pregnant. etc. :-) :-) > Expectations for Beth and millions of other students must be aligned > with the 21st-century demands of college and work, and we need to help > students meet those expectations. There are at least two things that are socially impossible. (1) Requiring that all people behave responsibly. (2) Requiring that all people educate themselves. > Personally - I think the we that needs to do more are the parents > (there I said the P word). Most really successful students that I have > ever had experience of knowing, the main reason (IMO) that they were as > successful as they were is due in a large part to their parents. ABSOLUTELY! Parents need to motivate their kids that education is important. And I don't just mean preparing for college education. Learning to be a good plumber/carpenter/auto mechanic/chef/ etc. is education as well. One problem with this is that parents who are poorly educated themselves generally do not teach their children that education is important. Stupidity is at least partially hereditary. [and we don't need a flame war about how much is environmental and how much is hereditary] So far, the presidential candidates in both parties have yet to > demonstrate the bold leadership and political courage Americans > deserve. In their news releases, speeches and town hall conversations, > they devote disturbingly little time to our nation's education crisis. Read. C.M. Kornbluth All the Marching Morons === Subject: Re: Students Leaving School Unprepared For College, Work Students Leaving School Unprepared For College, Work >I'm wondering how it was possible for my sister to have dropped out, had >a baby - and then go back after several years and get her GED and >successfully get through a 2 year college nursing program, all while >working a full time job and doing the day-to-day wife/family stuff. My >guess is my sister never used a microscope before college. > One word: MOTIVATION. Your sister seems to have had some. Which begs the question - why is it that some kids/people are not motivated and some are? > She does merit some kudos for persistence and diligence. I do too. > I would say well done to your sister except for one thing. I think it is irresponsible to have a baby before one gets > sufficiently > educated to support yourself and the baby. Life happens - the age she was and the sitation at home, it's not surprising that what happened happened. But she and the father did get married and have been for many years - heck, her one son just got married a last year and is expecting a baby sometime in Dec. During my time teaching, there were any number of pregnant students in my classes - at least one each year and AFAIK, not a one dropped out of school. > In fact, I think we should pass laws requiring a LICENCE before having > a baby. To obtain that license one should have to produce concrete > evidence that you are capable of supporting and caring for a baby. What sort of consequences are you imagining giving someone who didn't have a license and had a baby? Don't they do something like that in China? > Of course this is an unrealistic expectation and totally > unenforceable. And just not nice. Keep in mind, whatever you do would effect the baby, and it's not the baby's fault she/he was conceived. > [what would the punishment be? Jail? Taking the baby away? Either > one > dumps the problem of raising the child on the rest of society. I > vaguely > recall a science fiction short story in which licences were required. > If you > had an unlicenced baby you would have to defend your actions with your > life. > A volunteer would be selected from the public who would engage in > mortal > combat with the one who had the unlicensed baby. The objective there > was more > toward ZPG, but the idea was interesting; an unlicensed baby is > born, someone > dies == zero sum] An interesting idea ala J. Swift: How about if we make failure to be > responsible a crime? > examples of failure to be responsible would be: failing to educate > oneself, having a baby > one can't adequately support, drinking/doing drugs while pregnant. > etc. :-) :-) Also keep in mind, that not all of these situations turn out badly, my sister for an example. Just because there are a parade of bad examples presented on shows like Jerry Springer or Maury Povich doesn't mean each and every one ends up like that. Sometimes the perception of a problem is the problem. >Expectations for Beth and millions of other students must be aligned >with the 21st-century demands of college and work, and we need to help >students meet those expectations. > There are at least two things that are socially impossible. (1) Requiring that all people behave responsibly. > (2) Requiring that all people educate themselves. IMO, you can easily do both - key word is requiring, you can require people to do a lot of things, the rub is whether or not they actually do them. We require people to wear seatbelts, but still many people don't. >Personally - I think the we that needs to do more are the parents >(there I said the P word). Most really successful students that I have >ever had experience of knowing, the main reason (IMO) that they were as >successful as they were is due in a large part to their parents. > ABSOLUTELY! Parents need to motivate their kids that education is > important. And I don't just mean preparing for college > education. > Learning to be a good plumber/carpenter/auto mechanic/chef/ etc. > is education as well. Problem is, there are many parents who didn't have a positive experience with their own educational process. And there are others who didn't have any post-secondary education, and lack the personal experience to share with their kids. You want your kid to think about maybe becoming a plumber? Best way for that to happen is being one yourself. I would image that if you surveyed most people who are plumbers, you would probably find out that many of them went into the business simply because someone else in their family was in that business. > One problem with this is that parents who are poorly educated > themselves > generally do not teach their children that education is important. > Stupidity is > at least partially hereditary. [and we don't need a flame war about > how much is > environmental and how much is hereditary] If I was going to flame you on something, it would be the choice of the word stupid - such people are not stupid, they are simply ignorant. And it's not hereditary - and it's usually curable. Martin >So far, the presidential candidates in both parties have yet to >demonstrate the bold leadership and political courage Americans >deserve. In their news releases, speeches and town hall conversations, >they devote disturbingly little time to our nation's education crisis. > Read. C.M. Kornbluth All the Marching Morons > === Subject: Re: Students Leaving School Unprepared For College, Work One problem with this is that parents who are poorly educated > themselves > generally do not teach their children that education is important. > Stupidity is > at least partially hereditary. [and we don't need a flame war about > how much is > environmental and how much is hereditary] If I was going to flame you on something, it would be the choice of the > word stupid - such people are not stupid, they are simply ignorant. OK. They are simply ignorant. However, they should still act responsibly. They should ensure that their children are NOT ignorant by making sure that their children get educated. Or are you arguing that their ignorance is an excuse for failing in parental responsibility? > And it's not hereditary - and it's usually curable. Agreed. Ignorance is curable. But it requires motivation to do so. A parent might be ignorant. But it is still their job to see that their children do not grow up ignorant. And a failure to recognize that education is important *IS* stupidity. (IMO) As for stupid, it depends on the definition. Note that 50% of the population have below average intelligence. And I agree that there is no single measure of intelligence. I argue that having a bad educational experience yourself is not an excuse to pass on a bad attitude to your kids. A responsible adult learns from mistakes and tries to see that his/her children do not repeat those mistakes. === Subject: Re: Students Leaving School Unprepared For College, Work > One problem with this is that parents who are poorly educated >themselves >generally do not teach their children that education is important. >Stupidity is >at least partially hereditary. [and we don't need a flame war about >how much is >environmental and how much is hereditary] >If I was going to flame you on something, it would be the choice of the >word stupid - such people are not stupid, they are simply ignorant. > OK. They are simply ignorant. However, they should still act > responsibly. Define responsibly - seems to me that is a subjective concept, your definition and theirs (or mine) might not be the same. > They should ensure that their children are NOT ignorant by making sure > that their > children get educated. Or are you arguing that their ignorance is an > excuse for failing in parental responsibility? My guess is they never got their copy of the parental handbook that outlined their responsibilities. >And it's not hereditary - and it's usually curable. > Agreed. Ignorance is curable. But it requires motivation to do so. Eh, it some part - maybe. What it requires (IMO) is someone who isn't ignorant to educate them on what they don't know. Add to that, there needs to be some incentive to maybe make someone want to do something that from their POV really ain't all that necessary. > A parent might be ignorant. But it is still their job to see that > their > children do not grow up ignorant. Who (besides you) says it's their job - where exactly is this job description written? > And a failure to recognize that > education is important *IS* stupidity. (IMO) Keep in mind - that getting an education wasn't all that special of an experience for some people. > As for stupid, it depends on the definition. Note that 50% of the > population > have below average intelligence. Where did you get that statistic? Just curious. Seems to me that it would be more of a normal distribution (Bell curve) than a straight linear slope. > And I agree that there is no single > measure of > intelligence. Keep in mind, that even people with a genius level IQ can be ignorant about some knowledge. > I argue that having a bad educational experience yourself is not an > excuse to > pass on a bad attitude to your kids. Sure it is. You get food poisoning at a chain of local restaurants enough times, you're probably going to be less likely to encourage your kids to eat there. > A responsible adult learns from > mistakes and tries > to see that his/her children do not repeat those mistakes. Then we have a lot of irresponsible adults running around. Martin > === Subject: Simple formula needed Hi! Does anyone know how to fill in this formula in a form I could use in a programming language? Case: I need to find the angle in degrees from the center of a circle for a given point on a circle, this point always has the same distance from the center as the radius function AngleOfOuterPoint( X, Y, Radius) Anyone? === Subject: Re: Simple formula needed > Hi! Does anyone know how to fill in this formula in a form I could use in > a programming language? Case: I need to find the angle in degrees from the center of a circle > for a given point on a circle, this point always has the same distance > from the center as the radius > function AngleOfOuterPoint( X, Y, Radius) float CalcTheta( const JVEC2 Point1, const JVEC2 Point2 ) { float Theta = atan2( (Point2.x - Point1.x), (Point2.y - Point1.y) ); if ( Theta < 0 ) return 2 * PI + Theta; else return Theta; } In your case point1 is 0,0. This returns the angle in radians. There are 2 pi radians in a circle. I.E. 0.0 to 3.14159 * 2. So 1 degree = (2*pi) / 360.0 radians. Using computer math (sin, cos, tan, atan, etc...) the results will be in radians, not degrees. You either need to start thinking in radians, or do a lot of conversions. === Subject: Best Being Left Behind? courant.com/news/opinion/op_ed/hc- thorson1011.artoct11,0,6745926.column Best Being Left Behind? Robert M. Thorson October 11, 2007 There's only one certain way of not failing a test. Don't take it. That's what math and science educators believe is the real motive behind the Bush administration's decision to drop out of the next round of the TIMSS-A test (Trends in International Mathematics and Science Study). Given to graduating high school seniors, this test covers geometry, algebra and calculus, mechanics, electromagnetism, heat and atomic physics. Its purpose is to assess the competence of advanced students and compare performance internationally. I read of the dropout decision on Oct. 4, which just happened to be the 50th anniversary of Sputnik. Reflecting back, I'm glad that President Dwight Eisenhower didn't think that the best way not to lose the space race was not to take part. I was 6 years old when Sputnik orbited the earth. I remember searching the night sky for the satellite, being both excited and fearful. I remember throwing dozens of crab apples over the rounded crown of a tree, trying to mimic an orbital trajectory. Instead of being praised for my aeronautical simulations, I got in trouble for hitting the neighbor's car. I also remember the palpable tension in the adult air. The fear of falling behind the Communists induced the federal government to pour a river of money into science and math education. The result was a vast cohort of scientists who gave us not only Apollo and the moon, but the sinews of the information age. These are the anniversary reflections of Charles Krauthammer, opinion columnist for The Washington Post. I was a beneficiary of that river of money. Scientists became my heroes. I asked for chemistry sets, microscopes and backyard rockets for birthday presents. By the time I was awarded a Ph.D. in 1979, the United States had become a global science superpower. There is still federal support for math and science education. But this commitment is more about improving the scores of average and below-average students, rather than excellent ones. Consider the recent results from the National Assessment of Educational Progress, which evaluates those ages 9, 13 and 17 in mathematics. Between 1986 and 1999 there was a slow but steady improvement for 13- year-olds doing simple (Level 250) and moderately complex (Level 300) 17-year-olds, the scores have been mostly flat throughout that highest level of proficiency (Level 350), which looks like typical high school math to me. The good news in these exam results is the greater cultural parity and functional knowledge for the average fourth- and eighth-graders. The bad news is the decline in achievement for high-achieving high schoolers, a trend that would likely be manifested by the international test the U.S. Department of Education plans to skip. I do not accept the argument that they can't afford the $5 million to $10 million entry fee because this once-per-decade cost is less than the cost for a single hour of the Iraq war. Could it be that our nation is reversing the post-Sputnik trend of putting brains ahead of brawn? The administration also argues that that the international reference group against which the U.S. will be tested is not the group to which we should be compared. Russia and Iran are in that group. Should we not be concerned that our highest-achieving students are falling behind these nations? Even Slovenia outperformed the U.S. the last time the test was given (1995). That year, we were dead last in physics. Math educators are particularly up in arms about dropping out of the test. On record opposing the administration's decision are the National Council of Teachers of Mathematics, the Mathematical Association of America and the American Mathematical Society. The National Board for Education Sciences is calling for a review. Rising performance levels on math and physics tests can mean one of two things. It can mean either higher average test scores, or higher scores for high achievers. I would not want to think that leaving no child behind comes at the cost of not letting advanced students get ahead. Robert M. Thorson is a professor of geology at the University of Connecticut's College of Liberal Arts and Sciences and a member of The Courant's Place Board of Contributors. His column appears every Thursday. He can be reached at profthorson@hotmail.com. === Subject: Fast Math - Numeric Conversions such as Weight, Volume, Roman Numerals, etc at www.fast-math.org Enjoy! === Subject: Extending 2d regression algorithm into 3d I posted this message in alt.math.recreational 2 days ago but got no response. Am hoping for better luck here. Hi. I'm working on a 3D graphics modeling project (in my spare time for fun). At one point I want to find a line/cylinder that fits through a set of 3d points. I've found the source for 2D (x and y) but am not a math guru so was wondering if someone knew what I'd need to do to extend it into 3d (also using z). RegressionLine::RegressionLine(Points & points) { int n = points.size(); if (n < 2) throw (string(Must have at least two points)); double sumx=0,sumy=0,sumx2=0,sumy2=0,sumxy=0; double sxx,syy,sxy; // Conpute some things we need map::const_iterator i; for (i = points.begin(); i != points.end(); i++) { double x = i->first; double y = i->second; sumx += x; sumy += y; sumx2 += (x * x); sumy2 += (y * y); sumxy += (x * y); } sxx = sumx2 - (sumx * sumx / n); syy = sumy2 - (sumy * sumy / n); sxy = sumxy - (sumx * sumy / n); // Infinite slope_, non existant yIntercept if (abs(sxx) == 0) throw (string(Inifinite Slope)); // Calculate the slope_ and yIntercept slope_ = sxy / sxx; yIntercept_ = sumy / n - slope_ * sumx / n; // Compute the regression coefficient if (abs(syy) == 0) regressionCoefficient_ = 1; else regressionCoefficient_ = sxy / sqrt(sxx * syy); } I kinda even understand what this is doing. Well, no I don't. If I did I could probably extend it into the third dimention easily. One thing I'm looking at is the possibility of doing the exact same thing again, except that for x and y do it for x and z and then y and z, then I'd wind up with 3 slopes and I'd have to merge them into one 3d line somehow. Any help? === Subject: Re: who is right, wolfram or me? >hi, surfed into the wolfram integrator >(http://integrals.wolfram.com/index.jsp) >I entered x^2/(x-1) and pressed compute. Got this: >1/2(x-1)(x+3) + log(x-1). when I integratd myself mechanically I got: >x^2/(x-1)=>x^3/3 + ln(x-1). >all good, for input of x=2 I got 2.666667 while wolfram told me exactly 2.5, >who is right? is this a round off error at wolfram or is the formula there >wrong? > Have you tried differentiating to see which one gets you back to the original? Remove del for email === Subject: =?windows-1256?B?yNTR7SDTx9HlIC0g0dPHxuEg4eHM5sfhIOPMx+TtySDa4e0gz+3P7SDP7d3 t z+0gLSDY0e3eySDFzcrTx8ggx+Hk3sfY?=