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Math Help - number of bijection from A to B

  1. #1
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    number of bijection from A to B

    Let A and B be sets such that |A|=|B|=m. What is the number of bijections from A to B?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by santiagos11 View Post
    Let A and B be sets such that |A|=|B|=m. What is the number of bijections from A to B?
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    never mind I got it. Suppose |A|=|B|=m. Then we have a bijection iff we have injection. Since there are m! injections, we have m! bijections.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by santiagos11 View Post
    never mind I got it. Suppose |A|=|B|=m. Then we have a bijection iff we have injection. Since there are m! injections, we have m! bijections.
    Or! You can note that a bijection and a permutation are in fact the same (for finite cases...the infinite case holds but with a slightly different meaning). Thus, how many ways are there to permute m objects? [tex]m![/math\
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