Let *S* be a set. A *permutation* of *S* is a function from *S* to *S* that is both injective and surjective—in other words, a function that “rearranges” the elements of *S*. For example, if *S* = {1, 2, 3}, then the function *a* : *S* → *S* that sends 1 to 3, 2 to 1, and 3 to 2 is a permutation of *S*; so is the function *b* that sends 1 to 3, 2 to 2, and 3 to 1; whereas the function *c* that sends 1 to 3, 2 to 1, and 3 to 1 is not a permutation. An example of a permutation of the set of real numbers is the function *x* 8 - 2 ...

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