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.

## See also

Axiom of Choice
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## References

Renteln, P. and Dundes, A. "Foolproof: A Sampling of Mathematical Folk Humor." *Notices Amer. Math. Soc.* **52**, 24-34,
2005.## Referenced on Wolfram|Alpha

Zorn's Lemma
## Cite this as:

Weisstein, Eric W. "Zorn's Lemma." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ZornsLemma.html

## Subject classifications