Realvalued function/Set/Maximum/Definition

Let ${\displaystyle {}M}$ denote a set, and

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

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

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