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New page: The '''Well-Ordering Theorem''' was proved by Zermelos in 1904, and it states: <blockquote> Every set can be well-ordered. </blockquote> This result surprised mathematicians everywhere. B...
The '''Well-Ordering Theorem''' was proved by Zermelos in 1904, and it states:
<blockquote>
Every set can be well-ordered.
</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]].
[[Category: set theory]]
<blockquote>
Every set can be well-ordered.
</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]].
[[Category: set theory]]