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Whole Number

One of the numbers 1, 2, 3, ... (Sloane's 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
..., $-2$, $-1$, 0, 1, 2, ... integers Z
1, 2, 3, 4, ... positive integers Z+
0, 1, 2, 3, 4 ... nonnegative integers Z*
$-1$, $-2$, $-3$, $-4$, ... negative integers Z-

See also Counting Number, Fractional Part, Integer, N, Natural Number, Z, Z+, Z+, Z*


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 ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein