Natural Number
In mathematics, the natural numbers are the ordinary whole numbers used for counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively (see English numerals). A later notion is that of a nominal number, which is used only for naming.
Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics.
There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, with the latter definition having first appeared in the 19th century. Some authors use the term "natural number" to exclude zero and "whole number" to include it; others use "whole number" in a way that excludes zero, or in a way that includes both zero and the negative integers.
Read more about Natural Number: History of Natural Numbers and The Status of Zero, Notation, Algebraic Properties, Properties, Generalizations, Formal Definitions
Famous quotes containing the words natural and/or number:
“Doubtless, we are as slow to conceive of Paradise as of Heaven, of a perfect natural as of a perfect spiritual world. We see how past ages have loitered and erred. “Is perhaps our generation free from irrationality and error? Have we perhaps reached now the summit of human wisdom, and need no more to look out for mental or physical improvement?” Undoubtedly, we are never so visionary as to be prepared for what the next hour may bring forth.”
—Henry David Thoreau (1817–1862)
“Today, almost forty years later, I grow dizzy when I recall that the number of manufactured tanks seems to have been more important to me than the vanished victims of racism.”
—Albert Speer (1905–1981)