TOPICS
Search

Zorn's Lemma


If S is any nonempty partially ordered set in which every chain has an upper bound, then S 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

Explore with Wolfram|Alpha

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