Definition:Supremum of Sequence

Definition
A special case of a supremum of a mapping is a supremum of a sequence, where the domain of the mapping is $\N$.

Let $\struct {T, \preceq}$ be an ordered set.

Let $\sequence {x_n}$ be a sequence in $T$.

Let $\set {x_n: n \in \N}$ admit a supremum.

Then the supremum of $\sequence {x_n}$) is defined as:
 * $\displaystyle \map \sup {\sequence {x_n} } = \map \sup {\set {x_n: n \in \N} }$

Also see

 * Definition:Infimum of Sequence