Definition:Bounded Above Sequence/Real

Definition

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

Then $\sequence {x_n}$ is bounded above if and only if:

$\exists M \in \R: \forall i \in \N: x_i \le M$

Unbounded Above

$\sequence {x_n}$ is unbounded above if and only if there exists no $M$ in $\R$ such that:

$\forall i \in \N: x_i \le M$