Difference between revisions of "Well-Ordering Theorem"
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(That wasn't even a proper sentence, but I think this is what the author had in mind.) |
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''Every set can be well-ordered''. | ''Every set can be well-ordered''. | ||
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| − | This result surprised [[mathematician]]s everywhere. | + | 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]] | ||
Revision as of 20:35, December 2, 2008
The Well-Ordering Theorem was proved by Zermelos in 1904, and it states:
Every set can be well-ordered.
This result surprised mathematicians everywhere. The Well-Ordering Theorem is equivalent of the Axiom of Choice, and no well-ordering relation has ever been explicitly constructed for uncountable sets. Thus, the mathematicians who reject the Axiom of Choice also reject this theorem.