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Natural Number

A Positive Integer 1, 2, 3, ... (Sloane's A000027). The set of natural numbers is denoted N or Z+. Unfortunately, 0 is sometimes also included in the list of ``natural'' numbers (Bourbaki 1968, Halmos 1974), and there seems to be no general agreement about whether to include it.

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, Integer, N, Positive, Z, Z-, Z+, Z*


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

Courant, R. and Robbins, H. ``The Natural Numbers.'' Ch. 1 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 1-20, 1996.

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