# Definition:Increasing/Sequence/Real Sequence

## Definition

Let $\sequence {x_n}$ be a sequence in $\R$.

Then $\sequence {x_n}$ is increasing if and only if:

$\forall n \in \N: x_n \le x_{n + 1}$

## Also known as

Some sources refer to such a sequence as (monotone) non-decreasing.

## Examples

### Example: $\sequence 1$

The first few terms of the real sequence:

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

are:

$1, 1, 1, 1, \dotsc$

$S$ is both increasing and decreasing.