elementary set theory - Prove that for any two sets $|X|$ and $|Y|$, either $|X|leq|Y|$ or $|Y|leq|X|$.

Monday 11 July 2016

elementary set theory - Prove that for any two sets $|X|$ and $|Y|$, either $|X|leq|Y|$ or $|Y|leq|X|$.

Prove that for any two sets $|X|$ and $|Y|$, either $|X|\leq|Y|$ or $|Y|\leq|X|$.

I know that there is a proof using Zorn's Lemma but I can't figure out how to do it.

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