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Topic: Given a set , is there a disjoint set with an arbitrary cardinality?
Replies: 28   Last Post: Dec 4, 2012 5:50 PM

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 Aatu Koskensilta Posts: 2,639 Registered: 6/28/08
Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted: Dec 3, 2012 11:51 AM

jaakov <removeit_jaakov@deleteit_ro.ru> writes:

> 1. k is not related to the cardinality of X.

> 2. Your lambda need not exist. To show that lambda exists, one has to
> show that a set may not contain arbitrarily large ordinals. Is it a
> known fact or simply false?

For any set A, lambda = U{ alpha in A | alpha is an ordinal} is an
upper bound on ordinals in A. Take the next k ordinals after lambda and

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

Date Subject Author
12/3/12 jaakov
12/3/12 forbisgaryg@gmail.com
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Carsten Schultz
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Carsten Schultz
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 Butch Malahide
12/3/12 jaakov
12/3/12 Butch Malahide
12/4/12 jaakov
12/4/12 forbisgaryg@gmail.com
12/4/12 William Elliot
12/4/12 forbisgaryg@gmail.com
12/4/12 William Elliot
12/4/12 William Elliot
12/4/12 jaakov
12/4/12 William Elliot
12/4/12 jaakov
12/4/12 Shmuel (Seymour J.) Metz
12/4/12 Spammer
12/4/12 jaakov