Definition:Bounded Above Sequence/Real

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

Then $\left \langle {x_n} \right \rangle$ is bounded above iff:
 * $\exists M \in \R: \forall i \in \N: x_i \preceq M$

Also see

 * Definition:Bounded Below Real Sequence
 * Definition:Bounded Real Sequence


 * Definition:Bounded Above Real-Valued Function, of which a bounded above real sequence is the special case where the domain of the real-valued function is $\N$.


 * Definition:Lower Bound of Real Sequence