# Definition:Empty Supremum

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## Definition

Let $\left({S, \preceq}\right)$ be an ordered set.

Then the **empty supremum** is the supremum $\sup \varnothing$.

## Also see

- Supremum of Empty Set is Smallest Element: the
**empty supremum**exists if and only if $\left({S, \preceq}\right)$ has a smallest element.