Dear 100 Hour Board,
Is zero even, odd, neither, or both? Or is that not even the right question? My GRE prep book said it's even, so I wanted your opinions.
(Who will say it's even because that seems symmetrical and pretty on a number line)
I would really love to see a convincing argument that it's odd.
Anathema tells me this statement hurts her soul, because math would have to be broken for 0 to be odd. Maybe I just want to watch the world burn.
Sorry about your soul, Anathema.
Anathema is spot on, and she beat me to it. Pebble says he's baffled you would ask this. The definition of an even number is that it is divisible by 2, with no remainders/decimals. Anything that isn't even is odd. So yeah, even though 0/1 and 0/3 are still 0, because 0/2=0, it's an even number. Through my own understanding, 0 also has to be even because when you use 0 as a placeholder in other numbers (10, 40, 7000, etc.) Those numbers are even, so it has to be even.
Does that bother me a little bit? Yes. Even though I know the definition and can't argue with it, zero in my head has always been neither even or odd, because 0 is strange and has its own properties and rules for life that are both awesome and confusing all at once. Like, how can you classify 0 if you can't do some of the basic stuff with it that you would normally do with even numbers? You can't divide by 0 to get even numbers. You can't multiply by 0 to get even numbers. Adding 0 does pretty much nothing, subtracting 0 does nothing, raising something to the power of 0 just makes it one... That's not the case for ANY other even numbers. You see? Zero is it's own beautiful strange creature. That's why it feels a little strange for it to be classified as even... because shouldn't it be its own category?
Obviously that's not a justification, and I can't change the fact that it's even by definition. But I will always be fascinated by zero.
0 is an even number. Also, this actually is not a matter of opinion. The definition of an even number is any integer where the result of that integer being divided by 2 is still an integer (∀ n∈ Z, n even iff n/2∈ Z). 0/2 = 0, which is still an integer. Hence 0 is even.
I would say that 0 is a pretty odd number. I mean, it's both nonpositive and nonnegative. 0/0 is whatever it wants to be, and that's pretty odd. The zero vector is in both the range and the kernel of linear transformations. Also, we always have to account for zero for calculations and proofs and make exceptions for it like changing a "less than" into a "less than or equal to". It is the only number that is completely in balance, always. The zero vector (though not always zero) is the additive identity, always! And zero isn't even nothing, it is the presence of nothing! tHat'S PRetTy OdD!