Date: Jan 22, 2013 6:49 AM
Author: Jesse F. Hughes
Subject: Re: ZFC and God
WM <mueckenh@rz.fh-augsburg.de> writes:

> On 21 Jan., 19:07, Zuhair <zaljo...@gmail.com> 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