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Topic: Whole, Natural, & Counting Numbers?
Replies: 5   Last Post: May 5, 2008 11:27 AM

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Alexander Bogomolny

Posts: 406
Registered: 12/4/04
Re: Whole, Natural, & Counting Numbers?
Posted: Oct 1, 2001 9:10 PM
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"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.

> I hope this clears it up for you.

Alexander Bogomolny,
http://www.cut-the-knot.com

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