Definition:Monotone (Order Theory)/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 monotone if it is either increasing or 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 monotone if it is either increasing or decreasing.

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

Also see

 * Strictly Monotone Sequence