
Re: ZFC and God
Posted:
Jan 22, 2013 3:18 PM


WM <mueckenh@rz.fhaugsburg.de> writes:
> On 22 Jan., 17:48, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: >> WM <mueck...@rz.fhaugsburg.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 it contains an infinite number. It doesn't. I mean that the cardinality of the set is greater than any finite number.
If you mean something else, then I see no reason to continue the discussion. You're simply badly confused on what one means when he says a set is infinite.
I'll snip the rest, because obviously you have shown no contradiction in ZF, since ZF does not prove that N contains a number bigger than any natural. You're just confused.
(Hint: if you think otherwise, you could start by citing a published theorem that ZF proves N contains an element larger than every finite number. I'll wait for it.)
 "If your community has been lying about my research hoping I'd never find a way to prove that with some super dramatic discovery that's almost yanked out of the clear blue because I am a great discoverer then yeah, maybe you should worry."James S. Harris: great discoverer

