# Difference between revisions of "Infinite"

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* A set is infinite if it can be put into [[bijection]] with one of its proper [[subset]]s. | * A set is infinite if it can be put into [[bijection]] with one of its proper [[subset]]s. | ||

* A set is infinite if it is not empty and cannot be put into bijection with any set of the form <math>\{1, 2, \ldots, n\}</math> for a [[positive integer]] <math>n</math>. | * A set is infinite if it is not empty and cannot be put into bijection with any set of the form <math>\{1, 2, \ldots, n\}</math> for a [[positive integer]] <math>n</math>. | ||

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+ | ==Applications to Infinity with Sums== | ||

A sum works the same way. Certain sums equate to infinity, such as | A sum works the same way. Certain sums equate to infinity, such as |

## Revision as of 20:19, 18 June 2011

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 .

## Applications to Infinity with Sums

A sum works the same way. Certain sums equate to infinity, such as

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