Set Theory with Applications

A₁ A₂ axiom of choice B₁ B₂ bijection Boolean algebra Boolean functions called Cantor cardinal numbers Cartesian product Chapter completes the proof continuum hypothesis contradiction defined Definition denoted denumerable set disjoint equipotent equivalence relation Example finite cardinal numbers finite set function f G₁ given Hausdorff maximality principle hence implies infinite set initial ordinal integers least element Let f logic mathematical induction maximal element natural numbers nondenumerable nonempty set nonempty subset number of elements one-to-one correspondence order-isomorphic ordered pair partially ordered set partition power set Prob Problem proof of Theorem Prove the following rational numbers reader real numbers segment set theory surjective symbols Theorem 12 tion total order relation totally ordered set totally ordered subset transfinite cardinal number true truth table verify well-ordered sets well-ordering principle x'yz xy'z Zorn's lemma