Bijection

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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.


$\textbf{\underline{Examples:}}$


2008 AMC 12B Problems/Problem 22

2001 AIME I Problems/Problem 6

2006 AIME II Problems/Problem 4


This is recommended to be learned around the time you are introduced to the Ball-and-urn method, so that you can become increasingly familiar with the more advanced concepts of combinatorics.


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