# Definition:Negative/Real Number

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## 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.

## Sources

- 1960: Walter Ledermann:
*Complex Numbers*... (previous) ... (next): $\S 1.1$. Number Systems - 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $1$: Algebraic Structures: $\S 1$: The Language of Set Theory