# Definition:Monotone (Order Theory)/Sequence/Real Sequence

## Definition

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.

## Examples

### Example: $\sequence {\paren {-1}^n}$

The first few terms of the real sequence:

$S = \sequence {\paren {-1}^n}_{n \mathop \ge 1}$

are:

$-1, +1, -1, +1, \dotsc$

$S$ is not monotone, either increasing or decreasing.