A Dedekind-infinite set is clearly infinite, and in ZFC it can be shown that a set is Dedekind-infinite if and only if it is infinite.
It is consistent with ZF that there is an infinite set that is not Dedekind-infinite. However, the existence of such a set requires the failure not just of the full Axiom of Choice, but even of the Axiom of Countable Choice.
|Date of creation||2013-03-22 12:05:25|
|Last modified on||2013-03-22 12:05:25|
|Last modified by||yark (2760)|