Definition:Extended Real-Valued Function

Definition
Let $S$ be a set, and let $\overline \R$ denote the extended real numbers.

A mapping $f: S \to \overline \R$ is said to be an extended real-valued function.

Also known as
Some authors refer to extended real-valued functions as numerical functions.

However, the adjective 'numerical' is misleading, and so using this convention is discouraged.

Also see

 * Definition:Real-Valued Function