In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
Actually, YOU could not show that there are any inconsistencies in ZFC, even if there were any, as you have not enough mathematical skill to do so, as has been adequately demonstrated but your inadequate demonstrations of your many ant-mathematical claims. > > 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*.
Quite so! > > 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.
It does not have to "differ from all entries b_n at a finite place", but it does differ from each entry b_n at a finite place.
Which is an entirely different thing.
> 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.
Which claim again shows WM's incompetence. > > Therefore the diagonal does not increase the cardinal number of the > listed entries b_n.
The diagonal is not present in the list, if for no other reason than every member of WM's list has a last digit but the diagaonl does not. > > The diagonal may be infinitely long. But what does that mean? Every > given number of bits is surpassed. But the same holds for the entries > of the list.
Every member of the list has a last entry but the diagonal does not.
> The only difference could be a bit of the diagonal that > has no finite index.
Outside of WMytheology, one can have infinitely many indices without having an infinite index. --