# Natural number

*882*pages on

this wiki

A **natural number** is a positive (or nonnegative) integer. All the counting numbers, (1, 2, 3,...) are called natural numbers. Other possible names for the same type of object include whole number and counting number. The usage of these terms is not universally agreed upon, however, as it is possible for any of them to include or exclude zero from consideration.

The set of **natural numbers**, commonly denoted by , can be axiomatically defined by the Peano axioms. One way of *constructing* the natural numbers (or, more precisely, a sequence of objects that behave like the natural numbers) is through an iterative process starting from the empty set. See Wikipedia:Natural number for more information.

Natural numbers arise naturally (hence the name) from counting objects. Because of this fact, the elementary operations of arithmetic (addition, subtraction, multiplication and division) can be described in intuitively appealing ways for natural numbers before being extended to larger sets of numbers.