Meaning of Zorn's lemma

Zorn's' lem'ma

Pronunciation: (zôrnz), [key]
— Math. Math.
  1. a theorem of set theory that if every totally ordered subset of a nonempty partially ordered set has an upper bound, then there is an element in the set such that the set contains no element greater than the specified given element.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.