```Date: Jan 22, 2013 3:18 PM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

WM <mueckenh@rz.fh-augsburg.de> writes:> On 22 Jan., 17:48, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:>> WM <mueck...@rz.fh-augsburg.de> writes:>> > On 22 Jan., 15:49, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:>>>> > FIS: Finite Initial Segment>> > FISON: Finite Initial Segment Of Naturals (or indices)>>>> >> Well, it's not a "union" in the usual sense, but let's let it pass.>>>> > It is a union in that sense that every FISON {1, 2, ..., n+1} added>> > contains all smaler FISONs {1, 2, ..., n}.>>>> We were speaking about the real number d, not the set N.>> The set N is required to index the digits of the decimal fractions of> the real numbers.>>>> > This does never change. In particular the set is always finite. If>> > you add with always doubling frequence, you can add all FISONs in>> > finite time - given that an "all" is meaningfull here. But at the>> > end, you think, we cannot follow so quickly, and abracadabra we get>> > something larger than every FISON? Not in mathematics!>>>> Look, you need to offer an actual proof that>>>>   U_n=1^oo {1,...,n} is finite.>>>> I'll give you a hint, by showing you the proof that>>>>   U_n=1^oo {1,...,n} is infinite.>> Unfortunately you don't seem to understand what infinite means, in> particular that it has two different meanings.>>>> Just so you know what a proof looks like.>>>> Here's the proof.  First, let me be clear what I mean by infinite.  I>> mean that there is no natural k such that |U_n=1^oo {1,...,n}| = k.>> That is potential infinity. That proof is not necessary, because the> set is obviously potentially infinite. No, you shoudl give a proof,> that there is a larger k than all finite k.Er, no.  When I say that the union is infinite, I do not mean that itcontains an infinite number.  It doesn't.  I mean that the cardinalityof the set is greater than any finite number.If you mean something else, then I see no reason to continue thediscussion.  You're simply badly confused on what one means when hesays a set is infinite.I'll snip the rest, because obviously you have shown no contradictionin ZF, since ZF does not prove that N contains a number bigger thanany natural.  You're just confused.(Hint: if you think otherwise, you could start by citing a publishedtheorem that ZF proves N contains an element larger than every finitenumber.  I'll wait for it.)-- "If your community has been lying about my research hoping I'd neverfind a way to prove that with some super dramatic discovery that'salmost yanked out of the clear blue because I am a great discovererthen yeah, maybe you should worry."--James S. Harris: great discoverer
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