Definition:Decreasing/Sequence/Real Sequence

Definition
Let $\left \langle {x_n} \right \rangle$ be a sequence in $\R$.

Then $\left \langle {x_n} \right \rangle$ is decreasing iff:
 * $\forall n \in \N: x_{n+1} \le x_n$

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

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

Also see

 * Definition:Strictly Decreasing Real Sequence
 * Definition:Increasing Real Sequence
 * Definition:Monotone Real Sequence