Changes

The '''Well-Ordering Theorem''' was proved by Zermelos in 1904, and it states:

The '''Well-Ordering Theorem''' was proved by Zermelos in 1904, and it states:

<blockquote>

<blockquote>

Every set can be well-ordered.

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

</blockquote>

</blockquote>

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 set]]s, therefore many mathematicians have rejected the [[Axiom of Choice]].

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 set]]s, therefore many mathematicians have rejected the Axiom of Choice.

[[Category: set theory]]

[[Category: set theory]]