In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (i.e the positive integers or the counting numbers) or an element of the set {0, 1, 2, 3, ...} (i.e. the non-negative integers). The former is generally used in number theory, while the latter is preferred in mathematical logic, set theory and computer science. See below for a formal definition.
Natural numbers have two main purposes: they can be used for counting ("there are 3 apples on the table"), and they can be used for ordering ("this is the 3rd largest city in the country").
Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting, such as Ramsey theory, are studied in combinatorics.