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Math Help - number of functions

  1. #1
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    number of functions

    if i am asked the number of functions between {1,2,3}-> {1,2,3} then as the cardinality is the same all injective functions will be bijective and so also surjective and there are 6 of these, however i am given a formula that states the number of functions between two sets is X -> Y is |X|^|Y| which gives me 27 what have i done wrong here?
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  2. #2
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    Quote Originally Posted by hmmmm View Post
    if i am asked the number of functions between {1,2,3}-> {1,2,3} then as the cardinality is the same all injective functions will be bijective and so also surjective and there are 6 of these, however i am given a formula that states the number of functions between two sets is X -> Y is |X|^|Y| which gives me 27 what have i done wrong here?
    I am not at all sure that I understand what you are asking.
    But if B=\{1,2,3\} then there are 3^3 functions f:B\to B.
    Of those 27 functions there 3!=6 of them which are bijections.
    So what is your question now?
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  3. #3
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    well the six functions would be injective and surjective, so are the other 21 functions neither injective or surjective?
    thanks the help
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