Dan Bron wrote:
numbers; whenever convenient, it may be assumed that  0 e. P ."
>
>       Due to lack of standard terminology, the following terms and
>       notations are recommended in preference to "counting number,"
>       "natural number," and "whole number." ...
>

The disambiguating terms are what mathematicians normally use.  What is a
natural number depends on context.  I would favor including 0.  Whether
zero is included in the natural numbers is a similar argument as to
whether 1 is a prime.

> If I were God-King, I would mandate "natural numbers" indicate the
> positive integers, whole numbers are the integers, and would
> prohibit the use of the term "counting numbers".

"Counting numbers" suggests cardinal numbers, which certainly include 0,
but a lot more than the integers.

"Whole numbers" implies that the integers are embedded in the rational
numbers, which is by no means necessary.

Best wishes,

John Randall

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