If every chain in poset P has upper bound, P has maximal element. Equivalent to axiom-of-choice + well-ordering principle. Used to prove existence of bases in vector spaces, maximal ideals in rings, ultrafilters.
If every chain in poset P has upper bound, P has maximal element. Equivalent to axiom-of-choice + well-ordering principle. Used to prove existence of bases in vector spaces, maximal ideals in rings, ultrafilters.