Real numbers/Sequence/Increasing and decreasing/Definition

Increasing sequence

A real sequence ${\left(x_n\right)}_{n\in \mathbb{N}}$ is called increasing, if $x_{n+1}\ge x_n$ holds for all $n\in \mathbb{N}$, and strictly increasing, if $x_{n+1}>x_n$ holds for all $n\in \mathbb{N}$.

A sequence ${\left(x_n\right)}_{n\in \mathbb{N}}$ is called decreasing if $x_{n+1}\le x_n$ holds for all $n\in \mathbb{N}$, and strictly decreasing, if $x_{n+1}<x_n$ holds for all $n\in \mathbb{N}$.