Whole number

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The whole numbers are the nonnegative integers (0, 1, 2, 3, ...)

The set of all whole numbers is represented by the symbol [\mathbb] =

Algebraically, the elements of [\mathbb] form a commutative monoid under addition (with identity element zero), and under multiplication (with identity element one).

Aside

Unfortunately, this term is used by various authors to mean:

To remove ambiguity from mathematical terminology, those uses are now discouraged.

Whole number as nonnegative integer:

Bourbaki, N. Elements of Mathematics: Theory of Sets]. Paris, France: Hermann, 1968. ISBN 3540225250.
Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974. ISBN 0387900926.
Wu, H. Chapter 1: Whole Numbers. University of California at Berkeley, 2002. ["Notice that we include 0 among the whole numbers."]
The Math Forum, in explaining real numbers, describes "whole number" as ["0, 1, 2, 3, ..."].
Simmons, B. MathWords presents the whole numbers as ["0, 1, 2, 3, ..."] in a Venn diagram of common numeric domains.

Whole number as positive integer:

, [Whole Number] at MathWorld. (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:
- Beardon, Alan F., 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. ISBN 0395825172. Includes all three possibilities as definitions of "whole number."