Zorn's lemma

Mathematical proposition equivalent to the axiom of choice

Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered subset) necessarily contains at least one maximal element. The lemma was proven (assuming the axiom of choice) by Kazimierz Kuratowski in 1922 and independently by Max Zorn in 1935.

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