Infimum and supremum

In mathematics, the infimum or greatest lower bound of a set A, written as $\inf(A)$, is the greatest element among all lower bounds of A. Similarly, the supremum or least upper bound of A, written as $\sup(A)$, is the smallest element among all upper bounds of A.

For example, if A is the set $\{{\tfrac {1}{1}},{\tfrac {1}{2}},{\tfrac {1}{3}},\ldots \}$, then $\inf(A)=0$ and $\sup(A)=1$. Infimum and supremum are unique, if they exist. Infimum and supremum are key concepts in the field of mathematical analysis.

Related pages

• Maximum and minimum