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.

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.1$. Number Systems
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 1$: The Language of Set Theory
• 1971: Wilfred Kaplan and Donald J. Lewis: Calculus and Linear Algebra ... (previous) ... (next): Introduction: Review of Algebra, Geometry, and Trigonometry: $\text{0-2}$: Inequalities