Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
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 Logico-Philosophicus
|
|
|
|
