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Topic: Uncountable List
Replies: 8   Last Post: Dec 31, 2012 3:34 AM

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: Uncountable List
Posted: Dec 30, 2012 12:16 PM
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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,...).







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