Natural number
Natural numbers can be used for
counting (one apple, two apples, three apples, ...)
from top to bottom.
In mathematics, natural
numbers are the
ordinary counting numbers 1, 2, 3, ... (sometimes zero
is also included). There is no universal agreement about which set of numbers is designated by the
term "natural numbers": some use it to designate the positive integers{1, 2, 3, ...}, others include the
number 0, so that the term designates the non-negative integers {0, 1, 2, 3, ...}. The former
definition is the traditional one, the use of the
latter definition appears first 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.
Natural numbers have two main purposes: 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 more recent 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
.