Date: Dec 30, 2012 12:16 PM
Author: David C. Ullrich
Subject: Re: Uncountable List
On Sat, 29 Dec 2012 18:03:08 -0800, 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).

This is because c is also the cardinality of the set of

all binary sequences except (0,0,0,...).