# Zermelo’s postulate

If $\mathcal{F}$ is a disjoint family of nonempty sets, then there is a set $C$ which has exactly one element of each $A\in\mathcal{F}$ (i.e such that $A\cap C$ is a singleton for each $A\in\mathcal{F}$.)

This is one of the many propositions that are equivalent to the axiom of choice.

Title Zermelo’s postulate ZermelosPostulate 2013-03-22 13:13:36 2013-03-22 13:13:36 Koro (127) Koro (127) 6 Koro (127) Theorem msc 03E25 AxiomOfChoice MaximalityPrinciple TukeysLemma ZornsLemma KuratowskisLemma