My computer science teacher has a saying, "Mathematicians are always right." Why is zero even? Well, because it's
defined to be even. If you try to bring personal intuition into mathematics, you'll just repeatedly shoot yourself in the foot; there's no use arguing against it.
I had a similar problem with accepting that 1/inf = 0; to me, there could always be a smaller number, and therefore would never reach zero. Calculus made me realize I was wrong, and now I don't even bother trying to reason why mathematicians decided these things.
EDIT: Man, I knew as I wrote it that someone would get smart-ass with the sentence "Well, because it's defined to be even," but I didn't expect so many. Yes, you're right, zero isn't defined to be even, but zero meets the definition of evenness. Happy?
I had a similar problem with accepting that 1/inf = 0; to me, there could always be a smaller number, and therefore would never reach zero. Calculus made me realize I was wrong, and now I don't even bother trying to reason why mathematicians decided these things.
EDIT: Man, I knew as I wrote it that someone would get smart-ass with the sentence "Well, because it's defined to be even," but I didn't expect so many. Yes, you're right, zero isn't defined to be even, but zero meets the definition of evenness. Happy?