Infinite
From AoPSWiki
Revision as of 23:16, 22 April 2008 by I like pie (Talk | contribs)
A set 
is said to be infinite if there is a surjection 
. If this is not the case, is said to be finite.
In simplified language, a set is infinite if it doesn't end, i.e. you can always find another element that you haven't examined yet.
Equivalent formulations
- A set is infinite if it can be put into bijection with one of its proper subsets.
- A set is infinite if it is not empty and cannot be put into bijection with any set of the form
for a positive integer 
.
This article is a stub. Help us out by expanding it.
