Well-Ordering Theorem
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The Well-Ordering Theorem was proved by Zermelos in 1904, and it states:
Every set can be well-ordered.
This result surprised mathematicians everywhere. Because the Well-Ordering Theorem is a direct consequence of the Axiom of Choice, and no well-ordering relation has ever been explicitly constructed for uncountable sets, therefore many mathematicians have rejected the Axiom of Choice.
