# Is -3 a rational, irrational, natural, whole, integer or real number?

Jul 1, 2015

$- 3$ is an integer (and thus also rational and real)

#### Explanation:

natural or whole numbers (the terms are generally considered synonymous) are non-negative "counting numbers". Occasionally they are denoted by the symbol $\mathbb{N}$. There are some differences in definitions which sometimes include $0$ and sometimes exclude $0$ from $\mathbb{N}$.

$- 3$ is negative so it is not a natural or whole number.

integers are natural numbers extended to include negative versions of all the natural numbers (and $0$ if it were excluded by the "natural number definition"). The normal symbol for integers is $\mathbb{Z}$

$- 3$ obviously falls in this category.

Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. Rational numbers are denoted $\mathbb{Q}$.

Since $- 3$ can be written as $\frac{- 3}{1}$, it could be argued that $- 3$ is also a real number.

Irrational numbers are numbers that can not be expressed as a ratio (or fraction) of two integers but could represent a linear distance.

Real numbers are a union of both rational and irrational numbers