Definition:Bounded/Sequence
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< Definition:Bounded(Redirected from Definition:Bounded Sequence)
Definition
A special case of a bounded mapping is a bounded sequence, where the domain of the mapping is $\N$.
Let $\left({T, \preceq}\right)$ be a poset.
Let $\left \langle {x_n} \right \rangle$ be a sequence in $T$.
Then $\left \langle {x_n} \right \rangle$ is bounded iff $\exists m, M \in T$ such that $\forall i \in \N$:
- $m \preceq x_i$
- $x_i \preceq M$
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