Natural number

The set of natural numbers, denoted , is a subset of the integers . Unfortunately, exactly which subset is not entirely clear: in some texts, is taken to be the set of counting numbers (positive integers), while in others it is taken to be the set of whole numbers (nonnegative integers). Because of this ambiguity, one should always be careful to define one's notation clearly. Possible alternatives include for the non-negative integers and or for the positive integers (although is also sometimes used for the prime numbers). Natural numbers are important in the link between the well-ordering principle and the principle of mathematical induction.