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Topic: |R| > oo
Replies: 26   Last Post: Mar 8, 2013 8:55 PM

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Graham Cooper

Posts: 4,255
Registered: 5/20/10
Re: |R| > oo
Posted: Mar 8, 2013 8:55 PM
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On Mar 9, 10:46 am, William Hughes <wpihug...@gmail.com> wrote:
> There is a sequence the DIAGONAL cannot be.
> The DIAGONAL can be any sequence.
>
> GC tries to justify this!?!



Your claims are not computable

as infinite sequences never end.

By Induction on N for NxN lists DIAG=/=ANTI-ROW

By Induction on N-1 for NxN lists

|DIAG| = |ANTIDIAG| = 10^N-1 = ALL STRINGS

Your property of Unique Missing String is nullified.

Note |DIAG| as N->oo is computable

INF-STRING1 = INF-STRING2 is not computable.


-------------------

Your claim of GIVEN AN INFINITE LIST
you can CALCULATE A MISSING REAL

cannot be done by any Turing Machine that Halts.

It is ENTIRELY TRIVIAL that anything that follows
such a higher cardinality set theory are all based
on Non-Computable Axioms.

Herc
--
www.BLoCKPROLOG.com



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