Q&A: Why is Zero Considered Even?

by Justin Skycak on

An integer is even if it is twice some integer. Zero is even because zero is twice an integer, namely, zero is twice zero (0 = 2 x 0).

Cross-posted from here.

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I’ll provide the definition of “even” and then follow up with two examples, one of which is familiar (demonstrating that $6$ is even) and another of which is the thing being asked about (demonstrating that $0$ is even).

Definition of Even. An integer $n$ is even if it is divisible by $2$ with no remainder, meaning that it can be written in the form

$$\begin{align*} n = 2 \cdot a \end{align*}$$

where $a$ is an integer.

Familiar Example: $6$ is Even. The integer $n=6$ can be written as

$$\begin{align*} 6 = 2 \cdot 3 \end{align*}$$

(i.e., given $n=6,$ choose $a=3$). Therefore, $6$ is even.

Another Example: $0$ is Even. The integer $0$ can be written as

$$\begin{align*} 0 = 2 \cdot 0 \end{align*}$$

(i.e., given $n=0,$ choose $a=0$). Therefore, $0$ is even.


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