Zorn's Lemma

If is any nonempty partially ordered set in which every chain has an upper bound, then has a maximal element. This statement is equivalent to the axiom of choice.

Renteln and Dundes (2005) give the following (bad) mathematical jokes about Zorn's lemma:

Q: What's sour, yellow, and equivalent to the axiom of choice? A: Zorn's lemon.

Q: What is brown, furry, runs to the sea, and is equivalent to the axiom of choice? A: Zorn's lemming.

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