Talk:Equivalent Conditions for Dedekind-Infinite Set

There seems to be two things that are being stated here: one that Dedekind-infinite is equivalent to having the same cardinality as a proper subset.

The second (and more profound) thing is that you need ACC to prove that a set which has no bijection to a finite subset is necessarily Dedekind-infinite. That is, if ACC does not hold then there exist infinite sets which are not Dedekind-infinite.

So I suggest the two proofs be separated out into two pages. --prime mover 02:18, 5 April 2012 (EDT)