Definition:Monotone (Order Theory)/Sequence

From ProofWiki
Jump to navigation Jump to search

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


Also known as

This can also be called a monotonic sequence.


Also see


Sources