Obections to Cantor's Theory (Wikipedia article)
in [Logic]
|
Prev: Derivations
Next: Simple yet Profound Metatheorem
From: Alan Morgan on 28 Jul 2005 02:02 In article <MPG.1d51c4219426ae86989fd5(a)newsstand.cit.cornell.edu>, Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: >Daryl McCullough said: >> Tony Orlow says... >> >> >despite the fact that an infinite set of whole numbers requires >> >infinite whole numbers >> >> That's false, no matter how many times you say it. No finite >> set can contain every (finite) natural. Why? Because every finite >> set of naturals has a largest element, and there is no largest >> finite natural. >That's false, no matter how many times you say it. Which part do you disagree with? Do you disagree that every finite set of naturals has a largest element or do you disagree that there is no largest finite natural? Alan -- Defendit numerus
From: Virgil on 28 Jul 2005 02:51 In article <MPG.1d51c8215386c4f2989fd9(a)newsstand.cit.cornell.edu>, Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > Daryl McCullough said: > > Tony Orlow (aeo6) wrote: > > > > >Robert Low said: > > > > > >> OK, so how many elements are there in the set of all finite > > >> natural numbers? > > >> > > >Some finite, indeterminate number. You tell me the largest finite > > >number, and that's the set size. > > > > So you really think that there is some number n such that n is > > finite, but if you add 1 you get an infinite number? > (sigh) This is the last time I answer this question > NOOOOOOOOOOO!!!!!!!!! But since every natural has an immediate successor, and except for the first. an immediate predecessor, and there are no gaps( at least if one accepts Peano), the only way of getting from finite to infinite is by adding 1 to some finite natural to get an infinite natural. > > Maybe it's 7? Maybe 7 is the largest finite number, and 8 is > > actually infinite? > Don't be stupid. He is just trying to come down to your level, TO. > > > > In fact, a set is finite if and only if the number of elements is > > equal to a natural number. There is no largest natural number, and > > there is no largest finite set. The collection of all finite > > natural numbers is an infinite set. > The set of all finite numbers up to a given number has that number in > it, which is also the set size. Any subset of N has a size that is in > N. What member of N is the size of N? How about the size of N\{1}? The size of the set of even naturals or the size of the set of odd naturals? For the standard theory these all have trivially easy answers, and none of the sizes are members of N. For TO's theory it depends on how his medicatins are affecting him that day.
From: Keith Ramsay on 28 Jul 2005 02:53 Tony Orlow (aeo6) wrote: |If those lengths cannot be infinite, then the set cannot be either. Either you |have an upper bound or you do not, and if there is no upper bound on the values |of the members, then they may be infinite. If not, then what is the upper |bound, and how do you have an infinite set of strings with only finite lengths? Perhaps you're thinking that a restriction on the size has to come in the form of a dividing line, with the allowed lengths being on one side. There's a restriction, but not based on a dividing line. Finite lengths are allowed, but infinite lengths are not allowed. Since there's nothing in between finite and infinite, there's no point at which to draw a "dividing line". There is, nevertheless, a conceptual distinction between finite and infinite, which makes it possible to allow all finite lengths but forbid all infinite lengths. Keith Ramsay
From: Virgil on 28 Jul 2005 03:23 In article <iUXFe.297$Zh.52(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote in message > news:dc9f0t03cj(a)drn.newsguy.com... > >>> >Robert Low said: > >>> > > >>> >> OK, so how many elements are there in the set of all finite > >>> >> natural numbers? > > > > Tony replied. > > > >>>>Some finite, indeterminate number. > > > > That is an out-and-out contradiction. Let FN be the > > collection of all finite natural numbers. You say that > > FN is finite. You say that that means that its size is > > equal to some finite natural number. > > He never said that. He said "Some finite, indeterminate > number." He didn't say "Some finite, > indeterminate natural number." But even if he did, > mathematicians have their own meaning of words > and therefore his natural numbers might be different than > mathematicians. But TO insists that OUR natural numbers have to follow HIS rules, despite the fact that his rules contradict our rules on many issues. > > > So call that number > > L. If L is finite, then it must be an element of FN, > > because FN is the collection of *all* finite natural > > numbers. But that means that FN contains at least L+1 > > elements: 0, 1, 2, ..., L. That contradicts the claim > > that FN contains exactly L elements. > > Too bad he didn't imply that stuff. > > > Your theory is self-contradictory. Not that *you* would > > ever notice the contradiction, because you are just making > > things up as you go. You are just playing, not caring whether > > what you're saying makes sense or not. > > I think you are the one that is trying to put nonsense into his > post. No, just the one pointing it out! It was already there. There is a good deal of nonsense n all of TO's attempts to reformulate mathematics in his own image.
From: Virgil on 28 Jul 2005 03:25
In article <rZXFe.299$Zh.98(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote in message > news:dc9c6502t8a(a)drn.newsguy.com... > > > Basically, for any particular statement S, Tony will > > sometimes claim S, and sometimes claim the negation. > > Whichever one is most convenient for his argument. So > > sometimes there is a biggest finite natural, sometimes > > there isn't. Sometimes mathematical induction is valid, > > sometimes it isn't. Sometimes you use bijections to > > prove that sets are the same size. Sometimes you don't. > > Tony makes a model Cantorian. Show how little PJ knows. Cantorians have axiom systems which they agree upon. TO does not even agree with himself. |