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Topic: Uncountable Diagonal Problem
Replies: 52   Last Post: Jan 6, 2013 2:43 PM

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 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Uncountable Diagonal Problem
Posted: Dec 30, 2012 4:04 PM
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On Dec 30, 8:38 am, Shmuel (Seymour J.) Metz
<spamt...@library.lspace.org.invalid> wrote:
> In <Pine.NEB.4.64.1212300024480.22...@panix2.panix.com>, on 12/30/2012
>    at 12:47 AM, William Elliot <ma...@panix.com> said:
>

> >A list of length eta, is a function from the ordinals < beta to a
> >set of items.  Mega-sequence will be used as a synonym for list.

>
> Your definition of list is nonstandard. Why not use standard
> nomenclature, e.g., ordinal-indexed sequence
> <http://en.wikipedia.org/wiki/Order_topology#Ordinal-indexed_sequences>?
>

> >How long does a list without duplicates of infinite binary series
> >(IBS)  have to be to force the list to have every IBS?

>
> C+1[1]
>
> [1] Next largest cardinal, not next largest ordinal.
>
> --
> Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
>
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Formulate Cantor's nested intervals with "mega-sequences" (or
transfinite sequence or ordinal-indexed sequence) instead of sequences
of endpoints. Well-order the reals and apply, that the sequences
converge yet have not emptiness between them else there would be two
contiguous points, in the linear continuum. Note the identical
consequences, as to well-ordering the reals by the naturals.

Well-order the reals.

Regards,

Ross Finlayson

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