Date: Wed, 19 Nov 1997 02:15:57 0800
From: J Lillge
Hi.
That "cuttheknot" Web site is great! Nice job!
I have a question about some terminology used in:
This page presents the following definition:

"In the beginning there was counting
which gave rise to the natural numbers
(or integers): 1,2,3, and so on."
The next page (fundamental2.html) also includes statements consistent with this definition, such as:

"No such integer exists that when added
to 20 gives 4. We say that the set of
integers is not algebraicly closed."
and:

"To see how this works let's start with
integers (the set N of numbers 1,2,3,...)"
This definition of "integer" is different from the one I am accustomed to. In my research on mathematical terminology consistency, I have come to the following conclusions in this area:
The "cardinal" numbers are:

The set of the cardinalities of all finite sets.
{0,1,2,3,...}
The "positive integer" numbers are:

The set of the cardinalities of all nonempty finite sets.
{1,2,3,...}
The "negative integer" numbers are:

The set of values for x in the solutions to
all equations of the form x+n=0, where n is
any "positive integer" number. {1,2,3,...}
The "integer" numbers are:

The union of the set of "cardinal" numbers
and the set of "negative integer" numbers.

References:
http://www.pcwebopaedia.com/integer.htm
http://whatis.com/integer.htm
The "natural" numbers are:

The same as either the "cardinal" numbers or the
"positive integer" numbers, depending on the author.
The "whole" numbers are:

The same as either the "integer" numbers, the
"cardinal" numbers, or the "positive integer"
numbers, depending on the author.
Your comments on this significant terminology discrepancy regarding "integer" would be welcome.
 J. E. Lillge Software Architect Santa Clara Valley California