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