## SUPREMUM

### Supremum

In mathematics, the**supremum**of a subset

*S*of a totally or partially ordered set

*T*is the least element of

*T*that is

*greater than or equal to*all elements of

*S*. Consequently, the supremum is also referred to as the

**least upper bound**. If the supremum exists, it is unique, meaning that there will be only one supremum. If

*S*contains a greatest element, then that element is the supremum; otherwise, the supremum does not belong to

*S*. For instance, the negative real numbers do not have a greatest element, and their supremum is 0 .

*The above text is a snippet from Wikipedia: Supremum*

and as such is available under the Creative Commons Attribution/Share-Alike License.

and as such is available under the Creative Commons Attribution/Share-Alike License.

### supremum

#### Noun

- (
*of a subset*) the least element of the containing set that is greater or equal to all elements of the subset. The supremum may or may not be a member of the subset.

*The above text is a snippet from Wiktionary: supremum*

and as such is available under the Creative Commons Attribution/Share-Alike License.

and as such is available under the Creative Commons Attribution/Share-Alike License.