Is zero an even number?

Question

A quick google returns the answer on the parity of zero:

Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. The simplest way to prove that zero is even is to check that it fits the definition of "even": it is an integer multiple of 2, specifically 0 × 2.

So I know I've answered my own question but I still wanted to ask whether in some respects zero is the only number that is neither even nor odd?

Answer 1

Zero is even, as you argue. There's no circumstances where zero is taken to be odd, nor can it be taken to be neither odd nor even.

What is true is that $0$ is the only real number that is neither negative nor positive, alternatively the only real number $x$ such that $x = -x$.

Answer 2

"So I know I've answered my own question but I still wanted to ask whether in some respects zero is the only number that is neither even nor odd?"

There is a respect in which $0$ is neither even nor odd; since $\mathbb{Z}$ is an integral domain, it often makes sense to study the multiplicative structure of $\mathbb{Z} \setminus \{0\}$, and nevermind its additive structure. So we could, if we wanted to, define that an even number is an $x \in \mathbb{Z} \setminus \{0\}$ such that $2 \mid x$, in which case the statement "$0$ is even" is not true.

But, rather than redefining "even", its probably easier to just say: "$0$ is the only even number that isn't regular."