# Difference between revisions of "Bijection"

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A '''bijection''', or ''one-to-one correspondence '', is a [[function]] which is both [[injection|injective]] (or ''one-to-one'') and [[surjection|surjective]] (or ''onto''). A function has a [[Function#The_Inverse_of_a_Function|two-sided inverse]] exactly when it is a bijection between its [[domain]] and [[range]]. | A '''bijection''', or ''one-to-one correspondence '', is a [[function]] which is both [[injection|injective]] (or ''one-to-one'') and [[surjection|surjective]] (or ''onto''). A function has a [[Function#The_Inverse_of_a_Function|two-sided inverse]] exactly when it is a bijection between its [[domain]] and [[range]]. | ||

− | Bijections are useful in a variety of contexts. In particular, bijections are frequently used in [[combinatorics]] in order to count the elements of a set whose size is unknown. Bijections are also very important in [[set theory]] when dealing with arguments concerning [[infinite]] sets or in permutation and probability as seen in the 2008 Amc 12B problem 22. | + | Bijections are useful in a variety of contexts. In particular, bijections are frequently used in [[combinatorics]] in order to count the elements of a set whose size is unknown. Bijections are also very important in [[set theory]] when dealing with arguments concerning [[infinite]] sets or in permutation and probability as seen in the 2008 Amc 12B problem 22. |

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## Revision as of 10:11, 25 November 2016

A **bijection**, or *one-to-one correspondence *, is a function which is both injective (or *one-to-one*) and surjective (or *onto*). A function has a two-sided inverse exactly when it is a bijection between its domain and range.

Bijections are useful in a variety of contexts. In particular, bijections are frequently used in combinatorics in order to count the elements of a set whose size is unknown. Bijections are also very important in set theory when dealing with arguments concerning infinite sets or in permutation and probability as seen in the 2008 Amc 12B problem 22.

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