Q&A: Why is Zero Considered Even?

by Justin Skycak (x.com/justinskycak) on

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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