Let's start with the popular-but-wrong response; the one that would get the QI
alarm awooga-ing:

*"it's neither!"*

**Wrong!**

Now I've lit the blue touchpaper for a few ranty comments or tweets, let's
look at the facts. A good place to start is to take a step back and ask...

## What exactly is an even number?

The first port of call for almost all questions must surely be the great*
Wikipedia, which says that "

*an even number is an integer that can be divided by two and remain an integer or has no remainder.*"
Wikipedia isn't the best source for dissuading ranty comments, though.

Wolfram|Alpha, possibly a more reliable source of mathematical information in many eyes,
says "

*an even number is a number in the form $n = 2k$ where $k$ is an integer*."### Does zero fit here?

Wikipedia first:

- An integer is a number with no fractional part (i.e. no decimals; a whole number): ✓
- If we divide zero by 2 we get zero (with no remainder): ✓

And Wolfram|Alpha:

- If we can find an integer $k$ such that $0=2k$ that means $0$ is even:

$k = \frac{0}{2}$, so $k = 0$. ✓

Both Wikipedia and Wolfram|Alpha agree:

**$0$ is even.**

## Need some more?

- Back at primary school you may have learnt a quick way of identifying whether a number of any size is even by glancing at its units digit: any whole number that ends in $0, 2, 4, 6$ or $8$ is even, $0$ ends in... $0$. So it's even.
- Additionally, you might also recall the rule that if you add two even numbers together the result is always even, for example: \[2+2=4\] \[120 + 346 = 466\]

Well, $-2 + 2 = 0$, so $0$ is even. - It's also true that two odd numbers added together ($3 + 7$, for example) give an even number ($10$).

What's $-3 + 3$? Oh, it's $0$, so that's even. - Multiplicatively, any even number multipled by
*any integer*results in another even number, e.g.:

\[2 \times 3 = 6\] \[84 \times -37 = -3,108 \]

$28 \times 0 = 0$, so $0$ is even. - We're all familiar with the number line, stretching from $ -\infty $ to $ + \infty$ . Let's look at a section of that line with $0$ in it:... , -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, ...And let's colour in the even ones:... , -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, ...Without $0$ included there's a big hole and the pattern is broken. Why would we do that to a perfectly decent pattern?

## Still not sure?

Many a maths fan's bible, the

*On-line Encyclopedia of Integer Sequences*(OEIS) naturally includes an entry on*the nonnegative even numbers*and this begins with $0$. Are*you*going to argue with the OEIS?* And often, I admit, fallible