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natural number

A number used for counting: 1, 2, 3, .... The debate about whether zero should also be included as a natural number has been going on for hundreds of years, and there's no general agreement even today. To avoid confusion, 0, 1, 2, 3, ..., are often referred to as non-negative integers or whole numbers, while 1, 2, 3, ..., are called positive integers.

Adding or multiplying natural numbers always produces other natural numbers. However, subtracting them can produce zero or negative integers, while dividing them produces rational numbers. An important property of the natural numbers is that they are well-ordered, in other words, every set of natural numbers has a smallest element. The deeper properties of the natural numbers, such as the distribution of prime numbers, are studied in number theory. Natural numbers can be used for two purposes: to describe the position of an element in an ordered sequence, which is generalized by the concept of ordinal number, and to specify the size of a finite set, which is generalized by the concept of cardinal number. In the finite world, these two concepts coincide; however, they differ when it comes to infinite sets (see infinity).

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