Definition:Strictly Monotone/Sequence

From ProofWiki
Jump to navigation Jump to search

Definition

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


Then a sequence $\sequence {a_k}_{k \mathop \in A}$ of terms 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


Sources