```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 isnot part of the set of all terminal fractions and hence you haven'tshown that *this* enumeration is not surjective, much less that theset 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 ashame to your school.-- "And yes, I will be darkening the doors of some of you, sooner than youthink, even if it is going to be a couple of years, and when you lookin my eyes on that last day of work at your school, then maybe you'llunderstand mathematics."  -- James S. Harris on Judgment Day
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