The MathResource
Zorn's lemma,
n. the non-constructive set-theoretic result that, in an ordered set in which every chain has an upper bound, there is a maximal element. This is important in mathematical practice and equivalent to the axiom of choice, the well-ordering theorem, and the Hausdorff maximality theorem. (Named after the German-born American group theorist, algebraist, and analyst, Max August Zorn (1906-).)