## 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 .

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### supremum

#### Noun

1. (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
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