# Definition:Supremum

## Disambiguation

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Supremum may refer to:

## Also defined as

Some sources refer to the supremum as being the upper bound.

Using this convention, any element greater than this is not considered to be an upper bound.

## Also known as

Particularly in the field of analysis, the supremum of a set $T$ is often referred to as the least upper bound of $T$ and denoted $\map {\mathrm {lub} } T$ or $\map {\mathrm {l.u.b.} } T$.

Some sources refer to the supremum of a set as the supremum on a set.

Some sources refer to the supremum of a set as the join of the set and use the notation $\bigvee T$ or $\ds \bigvee_{y \mathop \in T} y$.

Some sources introduce the notation $\ds \sup_{y \mathop \in T} y$, which may improve clarity in some circumstances.

Some older sources, applying the concept to a (strictly) increasing real sequence, refer to a supremum as an upper limit.

## Also see

• Results about suprema can be found here.

## Linguistic Note

The plural of supremum is suprema, although the (incorrect) form supremums can occasionally be found if you look hard enough.