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 if and only if it is either strictly increasing or strictly decreasing.

Real Sequence

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

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

Then $\sequence {x_n}$ is strictly monotone if and only if it is either strictly increasing or strictly decreasing.

Also known as

This can also be called strictly monotonic.

Also see

• Definition:Increasing Sequence
• Definition:Decreasing Sequence
• Definition:Monotone Sequence

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): monotonic sequence