[Math] What are the “whole numbers”

Question

Just recently, I attempted to answer a question involving "whole numbers", but discovered that my long-held assumption (that they're the same as the integers), is not universal.

[In fact, it seems I owe a retraction for whenever I've snickered as a result of people claiming there are no "whole number" solutions to $a^n+b^n=c^n$ when $n>2$.]

Question: When it comes to the "whole numbers", who uses which definition?

I'm thinking geographically. E.g., since I've always equated whole numbers and integers, perhaps it's an Australian thing (or perhaps it's a "me" thing).

Question: Are there any rules-of-thumb as to who uses what definition?

This matters, because when I'm teaching, I sometimes say "whole numbers" while meaning "integers", and expect others to arrive at the same conclusions as me.

Answer 1

The Wikipedia page claims that "whole numbers" can refer to the integers, or the nonnegative integers, or the strictly positive integers. A hidden comment gives a few examples of each usage, which I reproduce below:

Whole number as nonnegative integer:

• Bourbaki, N. Elements of Mathematics: Theory of Sets. Paris: Hermann, 1968.
• Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974.
• The Math Forum, in explaining real numbers, describes "whole number" as "0, 1, 2, 3, ...".

Whole number as positive integer:

• The Math Forum, in explaining perfect numbers, describes whole number as "an integer greater than zero".
• Eric W. Weisstein. "Whole Number." From MathWorld—A Wolfram Web Resource. (Weisstein's primary definition is as positive integer. However, he acknowledges other definitions of whole number, and is the source of the reference to Bourbaki and Halmos above.)

Whole number as integer:

• Alan F. Beardon, Professor in Complex Analysis at the University of Cambridge: "of course a whole number can be negative..."
• The American Heritage Dictionary of the English Language, 4th edition, includes all three possibilities as definitions of whole number.
• Webster's Third New International Dictionary (Unabridged) has the following entry: "whole number n : INTEGER".