Date: Dec 30, 2012 10:22 PM
Author: William Elliot
Subject: Re: Uncountable List

On Sun, 30 Dec 2012, David C. Ullrich wrote:
> William Elliot <marsh@panix.com> wrote:
> 
> >How long does an uncountable list with no duplicates,
> >of infinite binary sequences (IBS) have to be to force 
> >the list to contain all the IBS's?
> 
> It's obvious that there is no length long enough to force this. A "list" 
> of length c (the cardinality of the set of infinite binary sequences) 
> need not contain all the sequences, and a list of length greater than c 
> must contain duplicates (and still need not contain all the sequences).

Whoops.

How long does an uncountable list have 
to be before it must contain a duplicate?