...that Show that • PROBLEM 7-33 (Axiom of Choice) => (Zorn's Lemma). ZORN'S LEMMA If (A, £,) is a partially ordered set, such that every chain in A...upper bound in A, then A contains a maximal element. According to the Hausdorff maximality principle, the non-empty partially ordered set (A, ¿) has a...

...previously defined notions occur is Zorn's Lemma: if A = < A, > is a poset and every subchain B of A has an upper bound in A, then A contains a maximal element. Passing through [ -¿ Graph] Path [ —+ Grapk Tree] Poset [ —¿ Partially ordered set] Principal...

...meat of thepreviouslydeflnednotionsoccurisZori¿sLemma:ifA= <A, > is a poset and every subchain B of A has an upper bound in A, then A contains a maximal element. Passing through [ -¿ Graph] Path [ —¿ Grapk Tree] Poset [ —¿ Partially ordered set] Principal...

...‘lemma' for historical reasons, but indeed it is just another formulation of the axiom of choice. Zorn's Lemma: if A is a nonempty partially ordered...that every chain in A has an upper bound in A, then A has a maximal element. This form of the axiom of choice is perhaps mostly applied in mathematics outside...