# Realvalued function/Set/Maximum and minimum/Definition

Maximum

Let denote a set, and

a
function.
We say that attains in a point
its * maximum*, if

and that attains in its * minimum*, if

Maximum

Let ${}M$ denote a set, and

- $f\colon M\longrightarrow \mathbb {R}$

a
function.
We say that ${}f$ attains in a point
${}x\in M$
its * maximum*, if

- $f(x)\geq f(x'){\text{ holds for all }}x'\in M,$

and that ${}f$ attains in ${}x$ its * minimum*, if

- $f(x)\leq f(x'){\text{ holds for all }}x'\in M.$