"C. McGinnis" wrote: > > The Natural ( or Counting ) Numbers are the first numbers you learn. They > are sometimes called the counting numbers because they are the numbers you > count with. I.e. 1, 2, 3, 4, ...
That's good. The terminology is rooted in the experience. > > The Whole Numbers includes all of the Natural numbers with the addition of > 0.
This is more or less correct. But, for example, The Harper Collins Dictionary of Mathematics says this:
whole number, another term for a NATURAL NUMBER, usually including zero. Usage, however, varies, and the term may be used for all INTEGERS, or only positive integers.
> Zero is not a Natural Number because it is not a counting number,
This is, by your definition, a tautology.
> and infact > was developed at a later time.
This is less important and, in fact, is not a part of the definition at all.
Historywise, the ancients did not think 1 is a number either, for the very reason you mention. There's no reason to count a single object. But this is true that zero is a late invention.
> (Or so they say.) You don't count to 3 > saying 0, 1, 2, 3.
But you do count backwards: 3, 2, 1, go. There's also a ground zero. The floors are very often counted as ground, first, second, etc.