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

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 Shmuel (Seymour J.) Metz Posts: 3,473 Registered: 12/4/04
Re: Uncountable Diagonal Problem
Posted: Dec 31, 2012 2:07 PM

In <50e06de8\$22\$fuzhry+tra\$mr2ice@news.patriot.net>, on 12/30/2012
at 11:38 AM, Shmuel (Seymour J.) Metz
<spamtrap@library.lspace.org.invalid> said:

>In <Pine.NEB.4.64.1212300024480.22883@panix2.panix.com>, on
>12/30/2012
> at 12:47 AM, William Elliot <marsh@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.

Whoops! As David pointed out, an ordinal-indexed sequence of reals of
cardinality C+1 must have duplicates.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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