Choice Function/Examples/Singletons

Example of Choice Function

Let $\FF$ be a set of singletons.

Then there exists a choice function on $\FF$.

Proof

Let $f: \FF \to \bigcup \FF$ be the mapping defined as:

$\forall \set a \in \FF: \map f {\set a} = a$

Then $f$ is trivially a choice function on $\FF$.

$\blacksquare$

Sources

• 1973: Thomas J. Jech: The Axiom of Choice ... (previous) ... (next): $1.1$ The Axiom of Choice