Realvalued function/Set/Maximum and minimum/Definition

Maximum

Let $M$ denote a set, and

$f:M⟶ℝ$

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

$f(x)\ge f(x^{\prime })\text{ holds for all }{x}^{\prime }\in M,$

and that $f$ attains in $x$ its minimum, if

$f(x)\le f(x^{\prime })\text{ holds for all }{x}^{\prime }\in M.$