Definition:Bounded Above Sequence/Real

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This page is about real sequences which are bounded above. For other uses, see Definition:Bounded Above.

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

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

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


Also see


Sources