elementary discrete mathematics courses sometimes leave students with the impression that the subject matter of set theory is no more than these properties. for more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. for an introduction to set theory at a higher level, see also axiomatic set theory, cardinal number, ordinal number, cantor–bernstein–schroeder theorem, cantor's diagonal argument, cantor's first uncountability proof, cantor's theorem, well-ordering theorem, axiom of choice, and zorn's lemma.