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Difference between revisions of "Natural number"

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The set of '''natural numbers''', denoted <math>\mathbb{N}</math>, is a subset of the [[integer]]s <math>\displaystyle\mathbb{Z}</math>.  Unfortunately, exactly which subset is not entirely clear: in some texts, <math>\mathbb{N}</math> is taken to be the set of [[counting number]]s ([[positive integer]]s), while in others it is taken to be the set of [[whole number]]s ([[nonnegative]] integers).  Because of this ambiguity, one should always be careful to define one's notation clearly.  Possible alternatives include<math>\mathbb{Z}_{\geq0}</math> for the non-negative integers and  <math>\mathbb{Z}_{>0}</math> or <math>\mathbb{P}</math> for the positive integers (although <math>\mathbb{P}</math> is also sometimes used for the [[prime number]]s).
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The set of '''natural numbers''', denoted <math>\mathbb{N}</math>, is a subset of the [[integer]]s <math>\mathbb{Z}</math>.  Unfortunately, exactly which subset is not entirely clear: in some texts, <math>\mathbb{N}</math> is taken to be the set of [[counting number]]s ([[positive integer]]s), while in others it is taken to be the set of [[whole number]]s ([[nonnegative]] integers).  Because of this ambiguity, one should always be careful to define one's notation clearly.  Possible alternatives include<math>\mathbb{Z}_{\geq0}</math> for the non-negative integers and  <math>\mathbb{Z}_{>0}</math> or <math>\mathbb{P}</math> for the positive integers (although <math>\mathbb{P}</math> is also sometimes used for the [[prime number]]s).
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Natural numbers are important in the link between the well-ordering principle and the principle of mathematical induction.

Revision as of 05:29, 25 November 2007

The set of natural numbers, denoted $\mathbb{N}$, is a subset of the integers $\mathbb{Z}$. Unfortunately, exactly which subset is not entirely clear: in some texts, $\mathbb{N}$ 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$\mathbb{Z}_{\geq0}$ for the non-negative integers and $\mathbb{Z}_{>0}$ or $\mathbb{P}$ for the positive integers (although $\mathbb{P}$ 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.

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