Definition:Strictly Monotone/Sequence

Definition

Let $\left({S, \preceq}\right)$ be a totally ordered set.

Then a sequence $\left \langle {a_k} \right \rangle_{k \in A}$ of terms of $S$ is strictly monotone if it is either strictly increasing or strictly decreasing.

Real Sequences

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

Let $\left \langle {x_n} \right \rangle$ be a sequence in $\R$.

Then $\left \langle {x_n} \right \rangle$ is strictly monotone if it is either strictly increasing or strictly decreasing.

Notes

This can also be called strictly monotonic.

Also see

• Increasing Sequence
• Decreasing Sequence
• Monotone Sequence

Sources

• Seth Warner: Modern Algebra (1965): $\S 14$