# Definition:Decreasing/Sequence/Real Sequence

## Definition

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

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

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

## Also known as

A decreasing sequence is also referred to as order-reversing.

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

## 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.