Difference between revisions of "Finite"

 
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A [[set]] is said to be '''finite''' if either it is the [[empty set]] or it can be put into bijection with a set <math>\{0, 1, 2, \ldots, n\}</math> for some [[nonnegative]] [[integer]] <math>n</math>.
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Informally, a [[set]] is said to be '''finite''' if it does not go on for ever.  That is, any set whose elements could (theoretically) be named, one by one, in a finite amount of time is finite.  Finite sets include the [[empty set]], which has zero elements, and every set with a [[positive integer]] number of elements.
  
In simpler terms, finite means to be not infinite, that is to be countable.
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Formally, a set is finite if it is the empty set or it can be put into bijection with a set <math>\{0, 1, 2, \ldots, n\}</math> for some [[nonnegative]] [[integer]] <math>n</math>.
  
 
==See also==
 
==See also==
 
* [[Infinite]]
 
* [[Infinite]]

Latest revision as of 10:11, 7 July 2006

Informally, a set is said to be finite if it does not go on for ever. That is, any set whose elements could (theoretically) be named, one by one, in a finite amount of time is finite. Finite sets include the empty set, which has zero elements, and every set with a positive integer number of elements.

Formally, a set is finite if it is the empty set or it can be put into bijection with a set $\{0, 1, 2, \ldots, n\}$ for some nonnegative integer $n$.

See also