Cantor Confusion
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From: Virgil on 29 Oct 2006 13:20 In article <1162138811.058202.202230(a)m73g2000cwd.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > The answer for any time t *before noon* is independent of the chosen > enumeration of the balls. Since the balls are identified by their "ennumeration", WM must mean that if one switches around the numbering before beginning, the overall result is unchanged.
From: Virgil on 29 Oct 2006 13:27 In article <1162139037.377997.299950(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > > In the first, he says that "standard mathematics contains a > > > contradiction". > > as ar as standard mathematics is derived from set theory an comes to > the conclusion of an empty vase at noon or an uncountable set of reals. > Classical mathematics is free of such contradictions. Classical math requires that a when a set of numbers corresponding to points on a directed line is bounded above that there be an least upper bound point on that line. from which one can prove uncountability of points on that line. > > My proof of the binary tree covers all possible theories. And it should > not cost you too much time to see that it is true. It will cost any sensible person more than his lifetime to reconcile WM's illusionary infinite binary trees with actual infinite binary trees.
From: Virgil on 29 Oct 2006 13:37 In article <1162139168.281239.183260(a)b28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > You need not tell that to me. You should tell that to Wolfgang > > Mueckenheim who insists that sqrt(2) does not exist because it is > > impossible to know all the decimals in its decimal expansion. > > It does not exist as a number. It has no b-adic representation. It > exists as a geometric entity. It is an idea. Being a "number" is nowhere defined as having to have a complete decimal expansion, except possibly by WM himself, but everyone knows how screwed up he is. Real numbers have two standard definitions generally accepted: (1) as Dedekind "cuts" (2) as equivalence classes of Cauchy sequences of rationalsmodulo the null sequences. WM has no generally accepted definition, so they are particular to him alone, and are of no weight elsewhere.
From: Virgil on 29 Oct 2006 13:40 In article <1162139518.021783.8550(a)f16g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > MoeBlee schrieb: > > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > Therefore I don't see any necessity to use a special language like ZFC > > > or NBG, but use mathematics which can be understood by any freshman. > > > > Since you decline to name any mathematicians who understand what you are > > saying and agree with it, please name a freshman who understands it and > > agrees with it. > > After you will have finished your first semester, you will understand > the binary tree without external help too, I am sure. But students who pass that first semester, at least under any tutelage except WM's, will disagree with WM's interpretations.
From: Virgil on 29 Oct 2006 13:46
In article <1162139843.746495.323730(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > William Hughes schrieb: > > > > > > > And once again WM deliberately confuses, "all positions are > > > > finite", with "there are a finite number of positions". > > > > > > There is no confusing! Every finite position belongs to a finite > > > segment of positions (indexes). If you don't believe that and assert > > > the contrary, then try to find a finite position which dos not belong > > > to a finite segment (of indexes). > > > > > > It is simply purest nonsense, to believe that "all positions are > > > finite" if "there are an infinite number of positions". Let us consider the infinite (unending) list of strings in which the nth term consists of a string of n 1's. While every string in this list is finite, the set of such strings is not. > > My above statement is true within any system which is free of self > contradictions. Which claim is trivially false. There are contradiction free systems in which WM's statement is not even expressible, much less true. |