# Is $0$ an even number? [duplicate]

I have noticed that it is useful to treat $0$ as an even number, and do so. Especially for patterns, puzzles, etc, if I develop a formula that works for something, and uses the parity of the number, then for my formula to work for something, I usually need to treat $0$ as even.

Is $0$ treated as an even number?

## marked as duplicate by Henning Makholm, Dando18, Sahiba Arora, Hans Lundmark, XamAug 1 '17 at 19:19

• Yes, it is. An even number, by definition, is divisible by $2$. – Alvin Lepik Aug 1 '17 at 14:35
• Googling it would take you literally 1 second. And you would immediately find answer on Wikipedia. – windircurse Aug 1 '17 at 14:41
• Is there some integer $k$ such that $2k=0$? Yes, so zero is even. Of course there are always situations where a positive number is needed, in which case $0$ would not be a suitable value. – Joffan Aug 1 '17 at 14:42

Yes, since $2 (0) = 0$. Any integer evenly divisible by 2 is even.
Yes, it is. So if $2 \mid x$, we call $x$ even.
And obviously, $2 \mid 0$.
The way we define a even number is as follows $$x\ is\ even \Leftrightarrow\exists k\in\mathbf{Z}(x=2k)$$ evidently $0=2(0)$ so yes $0$ is even.
$0$ is an integer multiple of 2.
But the zero function $f$ such that $\forall x\in \mathbb{R}, f(x)=0$ is odd and even!