Changes

''Every set can be well-ordered''.

''Every set can be well-ordered''.

</blockquote>

</blockquote>

This result surprised [[mathematician]]s 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 set]]s, therefore many mathematicians have rejected the Axiom of Choice.

This result surprised [[mathematician]]s everywhere.  The Well-Ordering Theorem is equivalent of the [[Axiom of Choice]], and no well-ordering relation has ever been explicitly constructed for [[uncountable set]]s. Thus, the mathematicians who reject the Axiom of Choice also reject this theorem.

[[Category: set theory]]

[[Category: set theory]]