Definition:Bounded Above Sequence/Real/Unbounded

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

$\left \langle {x_n} \right \rangle$ is unbounded above iff there exists no $M$ in $\R$ such that:
 * $\forall i \in \N: x_i \preceq M$