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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.
Yes, I misread your original question.
> 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 you have your desired Y.
 Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus



