Definition:Bounded Above Sequence

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

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

Then $\sequence {x_n}$ is bounded above :
 * $\exists M \in T: \forall i \in \N: x_i \preceq M$

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

Also see

 * Definition:Bounded Below Sequence
 * Definition:Bounded Sequence


 * Definition:Bounded Above Mapping, of which a bounded above sequence is the special case where the domain of the mapping is $\N$.