The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Uncountable List
Posted: Dec 31, 2012 1:55 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Dec 30, 9:22 pm, William Elliot <> wrote:
> On Sun, 30 Dec 2012, David C. Ullrich wrote:
> > William Elliot <> 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?

If you're still talking about lists of infinite binary sequences, then
the answer (assuming the axiom of choice) is the initial ordinal
omega_{alpha + 1} where alpha is the ordinal such that c =
aleph_{alpha}. But that's the answer given in the post you were
replying to, so I guess you're looking for some other kind of answer.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.