Maximum and Minimum

Given a set $S$ of numbers, the maximum is the largest element in $S$, and the minimum is the smallest element. For a function $f(x)$ defined on a set $D$, the maximum value is the largest value $f(x)$ takes for $x$ in $D$, and the minimum is the smallest.

Important properties

• A set may have a unique maximum and minimum, or none if the set is empty.

• If all elements are equal, the maximum and minimum are the same.

• For functions, maximum and minimum values may occur at endpoints or inside the domain.

• The difference between maximum and minimum is called the range.