Changes

In many undergraduate mathematics curricula, the Axiom of Choice is introduced early as a tool for solving problems. It often goes under one of its is equivalent to other guises, propositions such as [[Zorn's Lemma]] or the [[Well-Ordering Theorem]]. Students are taught it as a proof method, but often with little mention of the questionable nature of the axiom. Often, a full discussion of the [[paradox]]es that accompany the axiom is left to a higher (graduate) level special topics course in [[logic]], despite the fact that mathematicians in numerous fields may be tempted to use it and thus should be aware of its controversy. Undergraduate courses also neglect to adequately mention when the axiom is being invoked, giving a false sense that use of the axiom is incidental, rather than documenting its widespread nature in recent mathematical proofs.