Definition:Bounded Below Sequence/Real

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

Definition

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


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

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


Unbounded Below

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

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


Also see


Sources