# Zermelo’s well-ordering theorem

If $X$ is any set whatsoever, then there exists a well-ordering of $X$. The well-ordering theorem is equivalent to the Axiom of Choice.

 Title Zermelo’s well-ordering theorem Canonical name ZermelosWellorderingTheorem Date of creation 2013-03-22 12:58:55 Last modified on 2013-03-22 12:58:55 Owner yark (2760) Last modified by yark (2760) Numerical id 5 Author yark (2760) Entry type Theorem Classification msc 03E25 Synonym well-ordering principle Related topic EquivalenceOfTheAxiomOfChoiceAndTheWellOrderingTheorem Related topic EquivalenceOfTheAxiomOfChoiceAndTheWellOrderingTheorem2 Related topic HaudorffsMaximumPrinciple Related topic ZornsLemmeAndTheWellOrderingTheoremEquivalenceOfHaudorffsMaximumPrinciple Related topic ZornsLemmaAndTheWellOrderingTheoremEquiv