Definition:Upper Bound of Sequence

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

Let $\left({T, \preceq}\right)$ be a poset.

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

Let $\left \langle {x_n} \right \rangle$ be bounded above in $T$ by $H \in T$.

Then $H$ is an upper bound of $\left \langle {x_n} \right \rangle$.

Real Sequence
The concept is usually encountered where $\left({T, \preceq}\right)$ is the set of real numbers under the usual ordering: $\left({\R, \le}\right)$:

Also see

 * Definition:Bounded Above Sequence


 * Definition:Bounded Below Sequence
 * Definition:Lower Bound of Sequence


 * Definition:Bounded Sequence