Category:Bounded Sequences

This category contains results about Bounded Sequences.
Definitions specific to this category can be found in Definitions/Bounded Sequences.

A special case of a bounded mapping is a bounded sequence, where the domain of the mapping is $\N$.

Let $\struct {T, \preceq}$ be an ordered set.

Let $\sequence {x_n}$ be a sequence in $T$.

Then $\sequence {x_n}$ is bounded if and only if $\exists m, M \in T$ such that $\forall i \in \N$:

$(1): \quad m \preceq x_i$

$(2): \quad x_i \preceq M$

That is, if and only if it is bounded above and bounded below.