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 set of [[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 [[positive integer]]s (sometimes called [[counting number]]s in elementary contexts), while in others it is taken to be the set of [[nonnegative]] integers (sometimes called [[whole number]]s). In particular, <math>\mathbb{N}</math> usually includes zero in the contexts of [[set theory]] and [[abstract algebra | algebra]], but usually not in the contexts of [[number theory]]. When there is risk of confusion, mathematicians often resort to less ambiguous notations, such as <math>\mathbb{Z}_{\geq0}</math> and <math>\mathbb{Z}_0^+</math> for the set of non-negative integers, and <math>\mathbb{Z}_{>0}</math> and <math>\mathbb{Z}^+</math> for the set of positive integers. | The set of '''natural numbers''', denoted <math>\mathbb{N}</math>, is a subset of the set of [[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 [[positive integer]]s (sometimes called [[counting number]]s in elementary contexts), while in others it is taken to be the set of [[nonnegative]] integers (sometimes called [[whole number]]s). In particular, <math>\mathbb{N}</math> usually includes zero in the contexts of [[set theory]] and [[abstract algebra | algebra]], but usually not in the contexts of [[number theory]]. When there is risk of confusion, mathematicians often resort to less ambiguous notations, such as <math>\mathbb{Z}_{\geq0}</math> and <math>\mathbb{Z}_0^+</math> for the set of non-negative integers, and <math>\mathbb{Z}_{>0}</math> and <math>\mathbb{Z}^+</math> for the set of positive integers. | ||
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== See Also == | == See Also == | ||
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* [[Induction]] | * [[Induction]] | ||
* [[Well-ordering principle]] | * [[Well-ordering principle]] | ||
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[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Number theory]] | [[Category:Number theory]] | ||
Revision as of 11:31, 19 April 2008
The set of natural numbers, denoted 
, is a subset of the set of integers, 
. Unfortunately, exactly which subset is not entirely clear: in some texts, is taken to be the set of positive integers (sometimes called counting numbers in elementary contexts), while in others it is taken to be the set of nonnegative integers (sometimes called whole numbers). In particular, usually includes zero in the contexts of set theory and algebra, but usually not in the contexts of number theory. When there is risk of confusion, mathematicians often resort to less ambiguous notations, such as 
and 
for the set of non-negative integers, and 
and 
for the set of positive integers.
See Also
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