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




Re: Uncountable List
Posted:
Dec 30, 2012 12:16 PM


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,...).



