If $\infty$ was a number, would it be even, odd, neither or both? [on hold]

If $\infty$ was a number, would it be even, odd, neither or both? [on hold]

If Infinity ($\infty$) was a number, would it be even, odd, neither or
both? Here there is a little analogy with $0$ except that it is the fact
that $0$ is neither positive nor negative. So I can imagine that Infinity
is neither odd, nor even. But I'm I right?