Whole Number

One of the numbers 1, 2, 3, ... (OEIS A000027), also called the counting numbers or natural numbers. 0 is sometimes included in the list of "whole" numbers (Bourbaki 1968, Halmos 1974), but there seems to be no general agreement. Some authors also interpret "whole number" to mean "a number having fractional part of zero," making the whole numbers equivalent to the integers.

Due to lack of standard terminology, the following terms are recommended in preference to "counting number," "natural number," and "whole number."

set	name	symbol
..., , , 0, 1, 2, ...	integers	Z
1, 2, 3, 4, ...	positive integers	Z-+
0, 1, 2, 3, 4, ...	nonnegative integers	Z-*
0, , , , , ...	nonpositive integers
, , , , ...	negative integers	Z--

REFERENCES:

Bourbaki, N. Elements of Mathematics: Theory of Sets. Paris, France: Hermann, 1968.

Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974.

Sloane, N. J. A. Sequence A000027/M0472 in "The On-Line Encyclopedia of Integer Sequences."