(6) Asume Tukey (Let A be a nonempety set such that for all sets B, BEAO every finite subset of B belongs to A, then A has a maximal element with respect toc) Prove Zorn: Let C be any set such that every chain in C has an upper bound, then C contains a maximal element. Hint Let A = set of all chains in C and apply Tukey.

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.