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{ | + | 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). |
Revision as of 11:19, 4 August 2006
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).
