Definition:Bounded Above Sequence/Real

Definition
Let $\sequence {x_n}$ be a real sequence.

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

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