# Infimum and supremum

least (resp. greatest) of majoring (resp. minoring) elements of a partially ordered set (not necessarily existing in all sets)

In mathematics, the infimum or greatest lower bound of a set A, written as ${\displaystyle \inf(A)}$, is the greatest element among all lower bounds of A. Similarly, the supremum or least upper bound of A, written as ${\displaystyle \sup(A)}$, is the smallest element among all upper bounds of A.[1]

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

## References

1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-10-14.
2. Weisstein, Eric W. "Supremum". mathworld.wolfram.com. Retrieved 2020-10-14.
3. Weisstein, Eric W. "Infimum". mathworld.wolfram.com. Retrieved 2020-10-14.