Difference between revisions of "Infinite"
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A [[set]] <math>S</math> is said to be '''infinite''' if there is a [[surjection]] <math>f:S\to\mathbb{Z}</math>. If this is not the case, <math>S</math> is said to be [[finite]]. | A [[set]] <math>S</math> is said to be '''infinite''' if there is a [[surjection]] <math>f:S\to\mathbb{Z}</math>. If this is not the case, <math>S</math> is said to be [[finite]]. | ||
| − | In simplified language, | + | 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=== | ===Equivalent formulations=== | ||
Revision as of 16:46, 20 July 2006
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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 is not empty and cannot be put into bijection with any set of the form
for a positive integer 
.
for a 
.
