Definition:Strictly Negative/Number

Definition

The concept of strictly negative can be applied to the following sets of numbers:

$(1): \quad$ The integers $\Z$

$(2): \quad$ The rational numbers $\Q$

$(3): \quad$ The real numbers $\R$

The strictly negative integers are the set defined as:

$\ds \Z_{< 0}$

$:=$

$\ds \set {x \in \Z: x < 0}$

$\ds $

$=$

$\ds \set {-1, -2, -3, \ldots}$

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

The strictly negative rational numbers are the set defined as:

$\Q_{< 0} := \set {x \in \Q: x < 0}$

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

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.