Definition:Strictly Monotone/Sequence

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

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

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

Also known as
This can also be called strictly monotonic.

Also see

 * Definition:Increasing Sequence
 * Definition:Decreasing Sequence
 * Definition:Monotone Sequence