Natural Numbers

Date: 6/25/96 at 14:8:21
From: dude
Subject: Natural Numbers

There are "natural" numbers, but are there "artificial" numbers?

Johann W. Sarmiento Klapper - Colombia

Date: 6/25/96 at 17:7:57
From: Doctor Tom
Subject: Re: Natural Numbers

"Natural" numbers is just a name given by mathematicians to the
set of numbers 1, 2, 3, ..., and so on.

It's dangerous to think of the name "natural" as meaning "non-
artificial".  But it's too late to change some names of
number systems since they've been in use for hundreds of years,
and changing them would cause far more confusion than leaving
the names as they are.

A mathematician can define any class of objects and a set of
operations on those objects and study its behavior.  Some systems
of numbers are very useful, and have gotten a lot of study -
for example the integers that include the natural numbers, zero,
and the negative natural numbers: ... -3, -2, -1, 0, 1, 2, 3, ...
Or the rational numbers (fractions), et cetera.

All numbers are, in a sense, "artificial", but some sets are
very useful and other sets are not.

For example, if I define the "Doctor Tom" numbers to be the
same as the natural numbers except that when you add 5 and 8
you get 10332, that's a perfectly well-defined (but not very
useful) number system.

In mathematics, a name is used with a very precise meaning that
may have little to do with the meaning of the English word.  So
"irrational" numbers are not numbers that can't argue logically!

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/