[rkts]

Zero is not defined to be even. A number is even if it's twice some integer. Zero is twice an integer (namely 0), so it's even.

If you try to bring personal intuition into mathematics, you'll just repeatedly shoot yourself in the foot

I disagree. Intuition should always be foremost in mathematical understanding. You may have gotten a different impression from your math classes, and that IMO is a consequence of bad teaching.

I had a similar problem with accepting that 1/inf = 0

As you should; the statement is false. The limit of 1/x as x->infinity is zero, but there is no x at which the quotient "reaches" zero. In non-standard analysis, if x is positive infinite, then 1/x is positive infinitesimal, meaning it is infinitely close to, but still greater than zero.

[redcap]

"A number is even if it's twice some integer"

You could argue that is the mathematician's definition - I think this is covered in the article to an extent.

A layman's definition would be along the lines of that if you keep taking 2 objects from a collection of objects (e.g. apples), the smallest number you end up with is 2.

The number zero is a very handy mathematical trick that the Romans didn't grasp, I'm no surprised that concepts around it aren't easy to understand as I posit that it's =not= intuitive.

I'd also guess that there are maths teachers in schools who aren't mathematicians or aren't as well educated in maths as they could be.

[ErrantX]

A layman's definition would be along the lines of that if you keep taking 2 objects from a collection of objects (e.g. apples), the smallest number you end up with is 2.

Ummm I get 0. It surely depends on whether the layman makes a logic choice about his ability to remove the final 2 apples.

EDIT: by the way the other flaw in that example is you need a definition of "even" to start with; otherwise you could begin with 9 apples. :D