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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




Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 3, 2012 10:07 AM


Am 03.12.12 15:21, schrieb jaakov: > Given a set X and a cardinal k, is there a set Y such that card(Y)=k and > X is disjoint from Y? > > Is there a proof of this fact that works without the axiom of regularity > (= axiom of foundation) and does not assume purity of sets? >
I am not sure if I understand all of this.
Consider the class of all ordinals not in X. This is a wellordered proper class and hence has an initial segment which is order isomorphic to k. Take that initial segment.
hth
Carsten



