In mathematics, natural numbers are those used for counting and ordering.
Some authors begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, and others start with 1, corresponding to the positive integers 1, 2, 3, etc...
Properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics.
In common language, for example, in primary school, natural numbers may be called counting numbers to contrast the discreteness of counting to the continuity of measurement established by the real numbers.