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

WM <> writes:

> On 22 Jan., 17:48, "Jesse F. Hughes" <> wrote:
>> WM <> writes:
>> > On 22 Jan., 15:49, "Jesse F. Hughes" <> 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