# Definition:Negative/Real Number

## Definition

The negative real numbers are the set defined as:

$\R_{\le 0} := \set {x \in \R: x \le 0}$

That is, all the real numbers that are less than or equal to zero.

## Also known as

In order to remove all confusion as to whether negative real number is intended to mean strictly negative real number, the use of the term non-positive real number is often recommended instead.

The $\mathsf{Pr} \infty \mathsf{fWiki}$-specific notation $\R_{\le 0}$ is actually non-standard. The conventional symbols to denote this concept are $\R_-$ and $\R^-$, but these can be confused with the set $\set {x \in \R: x < 0}$, as well as notation for topological set closure.