Definition:Monotone (Order Theory)/Sequence

Definition
Let $\struct {S, \preceq}$ be a totally ordered set.

A sequence $\sequence {a_k}_{k \mathop \in A}$ of elements of $S$ is monotone it is either increasing or decreasing.

Real Sequence
The above definition for sequences is usually applied to real number sequences:

Also known as
This can also be called a monotonic sequence.

Also see

 * Definition:Strictly Monotone Sequence