Set theory MOC

Choice function

A choice function 𝑓 :𝑋 ↣⋃𝑋 on a set of inhabited sets 𝑋 is a function which “chooses” an element from each set 𝐴 ∈𝑋, set i.e.

(∀𝐴∈𝑋)[𝑓(𝐴)∈𝐴]

Within ZF, a choice function cannot be guaranteed unless an explicit rule can be given for choosing elements, e.g. the smallest element of well ordered sets. To guarantee the existence of a choice function for an arbitrary set of inhabited sets, the Axiom of Choice is required.

---

tidy | en | SemBr