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Re: Who's up for a friendly round of debating CANTORS PROOF?
Posted:
Aug 19, 2011 7:10 PM
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On Aug 20, 8:55 am, SPQR <S...@roman.gov> wrote:
> In article
> <07c4f31c-f445-4de8-8738-e3cc9ab8a...@w22g2000prj.googlegroups.com>,
> Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > You have not accounted for this anywhere in the proof. You merely
> > > > wave your hands and say "BUT IT WORKS ON ANY DIAGONAL!"
>
> > > Actually, it was Cantor that said it, and what Cantor said was that his
> > > method works on any listing of binary sequences. He never said anything
> > > like what you claim.
>
> > sure they work on any listing of binary sequences taken as an
> > individual dataset.
>
> > but the claims of missing elements should hold up for any given SET as
> > well as any given LIST.
>
> The standard way to establish COUNTABILITY of a set is to list its
> elements, i.e., create a surjection from N onto the set. Cantor's
> argument sows that this is not always possible.
>
> When impossible the relevant set is called uncountable. as is the set of
> all functions from |N to {m,w}
>
> > Cantor had 2 proofs didn't he?
>
> > Powerset and anti-diagonal.
>
> Actually, he has three proofs, but his first one, of the uncountability
> of a real interval, is doubtless beyond you comprehension.
well it seems I cannot mention digits, permutations, antidiagonals,
reals and numerous other aspects as they are deemed unrelated to his
proofs.
You however, gave 2 missing reals to my LISTS
0.01111111111100000000000...
and
0.11111111111100000000000...
Can you explain why you chose those particular binary digits in the
first binary place?
Herc
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