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Math Help - Question about functions...

  1. #1
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    Question about functions...

    What does it mean for a function to be constant in discrete math terms?

    For instance, if I have two sets of numbers

    D = {2, 3, 5, 7, 11, 13, 17, 23, 29, 31}
    R = {2, 4, 6, 8, 10}

    f: D -> R has 5^10 functions
    f: R -> D has 10^5 functions
    f: D -> D has 10^10 functions

    (Are these all correct?)

    But how many constant functions exist:

    f: D -> R
    f: R -> D

    And how many functions f: D -> R exist such that f(5) = f(11) = 8?
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  2. #2
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    Quote Originally Posted by Chirisu View Post
    What does it mean for a function to be constant in discrete math terms? For instance, if I have two sets of numbers
    D = {2, 3, 5, 7, 11, 13, 17, 23, 29, 31}
    R = {2, 4, 6, 8, 10}

    f: D -> R has 5^10 functions
    f: R -> D has 10^5 functions
    f: D -> D has 10^10 functions

    (Are these all correct?) YES!
    A constant function has a one element range.
    But how many constant functions exist:
    f: D -> R 5
    f: R -> D 10

    And how many functions f: D -> R exist such that f(5) = f(11) = 8? \color{blue}4^8
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  3. #3
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    Awesome, thanks!
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