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

Let $\left \langle {x_n} \right \rangle$ be a sequence in $T$.

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

Then the supremum of $\left \langle {x_n} \right \rangle$) is defined as:
 * $\displaystyle \sup \left({\left \langle {x_n} \right \rangle}\right) = \sup \left({\left\{{x_n: n \in \N}\right\}}\right)$

Also see

 * Definition:Infimum of Sequence