Choice Function/Examples/Doubletons of Real Numbers

Example of Choice Function
Let $\FF$ be a set of sets of the form $\set {a, b}$ where $a$ and $b$ are real numbers.

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

Proof
Let $f: \FF \to \bigcup \FF$ be the mapping defined as:
 * $\forall \set {a, b} \in \FF: \map f {\set {a, b} } = \map \min {a, b}$

where $\min$ denotes the minimum operation.

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