>Even numbers give you piles of two without one left over. Zero fails the first condition since it gives you no piles at all. But it doesn’t leave a pile of one

>Even numbers give you piles of two without one left over. Zero fails the first condition since it gives you no piles at all. But it doesn’t leave a pile of one, so it’s not really odd, either. This definition does not naively extend to negative numbers, which are anti-piles of things. You are right, of course, about definitions serving their purpose. In this case maintaining the symmetry of alternation requires 0 to be even, and that argument could even be extended to negative numbers. (Of course other numbers, like the rationals and reals, are pure fiction and can safely be ignored negative or otherwise.)