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"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