# Is zero a rational number?

Apr 3, 2016

Yes, though it's open to debate.

#### Explanation:

A rational number is a whole number divided by a whole number.

A whole number must be the sum of two other integers, as two integers can only ever make another integer.

Therefore, $0$ is an integer because it is $3 + \left(- 3\right)$, both of which are whole.

And so $0$ may be written as a whole number divided by a whole number as

$\frac{0}{1}$ or even $\frac{3 - 3}{1} = 0$

You can also think of $0$ being an integer because it falls in the arithmetic sequence ${a}_{n + 1} = {a}_{n} + 1$, where ${a}_{0}$ is the hypothetical lowest possible integer.