# Definition:Strictly Negative/Real Number

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## Definition

The **strictly negative real numbers** are the set defined as:

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

That is, all the real numbers that are strictly less than zero.

## Also denoted as

The $\mathsf{Pr} \infty \mathsf{fWiki}$-specific notation $\R_{<0}$ is actually non-standard. The conventional symbol to denote this concept is $\R_-^*$.

Note that $\R^-$ is also seen sometimes, but this is usually interpreted as the set $\set {x \in \R: x \le 0}$.

Some sources, particularly those whose treatment is topological, use $\bar \R_+$.

Some sources merely refer to this as **negative**, as their treatments do not accept $0$ as being either **negative** or positive.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $1$: Algebraic Structures: $\S 1$: The Language of Set Theory - 2000: James R. Munkres:
*Topology*(2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers