Talk:Well-Ordering Theorem

Have we defined well-order (i.e., M is well-ordered iff M is ordered and any non-empty subset A of M has a minimum) anywhere? --BRichtigen 17:35, 2 December 2008 (EST)

Contradiction

This article states: [1] "Well-Ordering Theorem was proved by Zermelos in 1904" [2] "The Well-Ordering Theorem is equivalent of the Axiom of Choice" [3] "mathematicians who reject the Axiom of Choice also reject this theorem"

But this is a contradiction. If [1] is correct (the theorem is proved) then by [2] The Axiom of Choice is true. If the Well-Ordering Theorem relies on the Axiom of Choice, then by [2], [1] is false as the axiom of choice is unproven.

In mathematics if something it is proven correctly then it would be foolish (and incorrect) for mathematicians to reject it. If the proof relies on the Axiom of Choice then it is not yet proven, or is proven *given* the axiom of choice.