From ProofWiki
Jump to navigation Jump to search


This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

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.