BulldogLowell:
You are not correct regarding the counting numbers.You are mixing oranges with your apple analogy.
Decimals do not exist in the set of integers, for example.
You're talking about representations of quantities.
I am talking about numbers in the abstract. Not the representation of quantity but the actual quantity itself. I don't mean the part that you read and write, but the part that you actually do math with.
If I have 3 apples and you have 3.0 apples, sure you represented yours with an integer, but we both have the same actual quantity of apples. If we traded, it would still be an even trade. Unless, of course, you were rounding.