Date: Jan 22, 2013 6:49 AM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

WM <> writes:

> On 21 Jan., 19:07, Zuhair <> wrote:

>> Doesn't that say that mathematics following ZFC is only grounded in
>> Mythology driven principles!
>> Doesn't that mean that ZFC based mathematics is too imaginary that
>> even if consistent still it is based and rooted in fantasy that cannot
>> really meet reality!

> ZFC is not consistent unless inconsistencies are defined to be no
> inconsistencies, distinctions need not be distinguishable,
> incomletenesses need not be incomplete, and so on.
> Consider, for instance, all terminating binary fractions b_n
> 0.0
> 0.1
> 0.00
> 0.01
> 0.10
> 0.11
> 0.000
> where some numbers are represented twice (in fact each one appears
> infinitely often). Constructing the diagonal d we find that d differs
> from *every* b_n *at a finite place*.
> Since the above list is complete, which is possible because all
> terminating fractions, as a subset of all fractions, are countable, it
> is impossible that the diagonal differs from all entries b_n at a
> finite place. If this was possible, the list would have a gap, namely
> a finite initial segment of d. That means, the diagonal up to every
> bit can be found in the list. And after every finite place there is
> nothing that could distinguish two numbers.
> Therefore the diagonal does not increase the cardinal number of the
> listed entries b_n.

This is your proof that ZF is inconsistent, is it?
> The diagonal may be infinitely long. But what does that mean?

It means that d is not a terminating fraction, you moron, so d is
not part of the set of all terminal fractions and hence you haven't
shown that *this* enumeration is not surjective, much less that the
set of terminal fractions is uncountable.

> Every given number of bits is surpassed. But the same holds for the
> entries of the list. The only difference could be a bit of the
> diagonal that has no finite index. But such bits are not part of
> mathematics and of Cantor's argument.

You are incapable of very basic mathematical reasoning. You are a
shame to your school.

"And yes, I will be darkening the doors of some of you, sooner than you
think, even if it is going to be a couple of years, and when you look
in my eyes on that last day of work at your school, then maybe you'll
understand mathematics." -- James S. Harris on Judgment Day