Obections to Cantor's Theory (Wikipedia article)
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From: Virgil on 27 Jul 2005 16:13 In article <MPG.1d517d8532843fab989fa5(a)newsstand.cit.cornell.edu>, Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > If you allow infinite whole numbers, as is required, suddenly this > whole "uncountability of the power set" vanishes in a puff of smoke. So does all of standard arithmetic, calculus, analysis, and their applications in the sciences. We would have to g back to before Newton, and work everything out from scratch. And TO is no Newton. The apple that fell on TO's head was a rotten one.
From: Daryl McCullough on 27 Jul 2005 15:55 Tony Orlow <aeo6(a)cornell.edu> said: >I tell you what. You refute my inductive proof that the set of naturals is >finite, without refuting your own proof, and then we'll talk. Post it again. But please pay attention to what a proof by induction *is*. A proof by induction has the following form: 1. Prove Phi(0). 2. Prove forall n in N, Phi(n) implies Phi(n+1). 3. Conclude forall n in N, Phi(n). So induction is a way of proving a *universally* quantitied statement. What Phi are you using for the statement "the set of naturals is finite"? That isn't a universally quantified statement. It doesn't make any sense to prove it by induction. Once again, induction only allows you to prove something of the form "For every natural number n, Phi(n)" -- Daryl McCullough Ithaca, NY
From: malbrain on 27 Jul 2005 16:15 David Kastrup wrote: > malbrain(a)yahoo.com writes: > > > David Kastrup wrote: > >> malbrain(a)yahoo.com writes: > >> > >> > malbr...(a)yahoo.com wrote: > >> >> Tony Orlow (aeo6) wrote: > >> >> > Some finite, indeterminate number. You tell me the largest > >> >> > finite number, and that's the set size. It doesn't exist? > >> >> > Well, then, I can't help you. > >> >> > >> >> >From websters 1913 dictionary: > >> >> > >> >> De*ter"mi*nate (?), a. [L. determinatus, p. p. of determinare. See > >> >> Determine.] > >> >> > >> >> 1. Having defined limits; not uncertain or arbitrary; fixed; > >> >> established; definite. > >> >> > >> >> > >> >> Thus "indeterminate" is the exact opposite of fine. You can't have it > >> >> both ways. > >> > > >> > Ooops. "indeterminate" is the exact opposite of finite. You've > >> > uncovered a contradiction about the count of elements in an > >> > infinite set that cannot be resolved from the definitions of > >> > finite and indeterminate. karl m > >> > >> Uh, no. "Indeterminate" just means unspecified, not infinite. > > > > Read the definition. Determinate=defined limit; > > indeterminate=undefined limit=infinite. > > Undefined limit is not the same as infinite. For example, in > programming languages indeterminate loop forms are those for which you > can't say in advance how often they will be run (i.e., while-loops, as > opposed to the determinate for-loops). Programming languages weren't invented in 1913. Please use analogies that are pre-Cantor. The opposite of "undefined-limit" is infinite. karl m
From: malbrain on 27 Jul 2005 16:18 malbr...(a)yahoo.com wrote: > David Kastrup wrote: > > malbrain(a)yahoo.com writes: > > > > > David Kastrup wrote: > > >> malbrain(a)yahoo.com writes: > > >> > > >> > malbr...(a)yahoo.com wrote: > > >> >> Tony Orlow (aeo6) wrote: > > >> >> > Some finite, indeterminate number. You tell me the largest > > >> >> > finite number, and that's the set size. It doesn't exist? > > >> >> > Well, then, I can't help you. > > >> >> > > >> >> >From websters 1913 dictionary: > > >> >> > > >> >> De*ter"mi*nate (?), a. [L. determinatus, p. p. of determinare. See > > >> >> Determine.] > > >> >> > > >> >> 1. Having defined limits; not uncertain or arbitrary; fixed; > > >> >> established; definite. > > >> >> > > >> >> > > >> >> Thus "indeterminate" is the exact opposite of fine. You can't have it > > >> >> both ways. > > >> > > > >> > Ooops. "indeterminate" is the exact opposite of finite. You've > > >> > uncovered a contradiction about the count of elements in an > > >> > infinite set that cannot be resolved from the definitions of > > >> > finite and indeterminate. karl m > > >> > > >> Uh, no. "Indeterminate" just means unspecified, not infinite. > > > > > > Read the definition. Determinate=defined limit; > > > indeterminate=undefined limit=infinite. > > > > Undefined limit is not the same as infinite. For example, in > > programming languages indeterminate loop forms are those for which you > > can't say in advance how often they will be run (i.e., while-loops, as > > opposed to the determinate for-loops). > > Programming languages weren't invented in 1913. Please use analogies > that are pre-Cantor. The opposite of "undefined-limit" is infinite. Ooops, again. The opposite of "defined-limit" is infinite. karl m
From: David Kastrup on 27 Jul 2005 16:18
Tony Orlow (aeo6) <aeo6(a)cornell.edu> writes: > You may feel I am "blowing it" but, despite the fact that a better > foundation in the methods and language would give me better leverage > with those in the field, I have not had any mistake pointed out to > me that I could identify as a mistake. Not for lack of trying. You have quantifier dyslexia: you don't understand the difference between "arbitrarily large" and "infinite", even though it has been explained in minute detail to you in language that an average tenth grader should be able to understand. You are wasting your time in a field where you suffer from fundamental disabilities. There are no paralympics for mathematicians. Choose another hobby. > Anyway, thanks for the advice and concern. I don't suppose you have > understood or agreed with any of my points? I must be on the wrong > planet. Just on the wrong hobby. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum |