Definition:Supremum of Real Sequence

Definition
Let $\left \langle {x_n} \right \rangle$ be a real sequence.

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 Real Sequence