Definition:Strictly Negative/Real Number

Definition
The strictly negative real numbers are the set defined as:
 * $\R_{< 0} := \left\{{x \in \R: x < 0}\right\}$

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

Also denoted as
The -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 $\left\{{x \in \R: x \le 0}\right\}$.

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.