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Math Help - injective functions

  1. #1
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    injective functions

    i got confused by this question seems relatively simple but dnt get it.
    how many non-injective functions are there from {1,2,3,4} to {1,2,3,4,5}? How many non-injective functions are there from {1,2,3,4,5} to {1,2,3,4}?

    thanks.
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  2. #2
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    Using a usual notation for sets of functions B^A  = \left\{ {f|f:A \mapsto B} \right\} \Rightarrow \quad \left| {B^A } \right| = \left( {\left| B \right|} \right)^{\left| A \right|}, then if A = \left\{ {1,2,3,4} \right\}\,\& \,B = \left\{ {1,2,3,4,5} \right\} there are 5^4 functions from A to B. Of those (5)(4)(3)(2) are injections. So how many non-injections are there?

    There are no injections from B to A. WHY?
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  3. #3
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    because B has more elements than A
    when you say (5)(4)(3)(2)..what do you mean.thanks
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  4. #4
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    Quote Originally Posted by skystar View Post
    when you say (5)(4)(3)(2)..what do you mean.thanks
    Multiply: (5)(4)(3)(2)=120!
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