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Math Help - Bijective, surjective, injective functions

  1. #1
    Senior Member Paze's Avatar
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    Bijective, surjective, injective functions

    A General Function points from each member of "A" to a member of "B".

    To be a function you never have one "A" pointing to more than one "B", so one-to-many is not OK in a function (as you would have something like "f(x) = 7 or 9")

    Injective, Surjective and Bijective

    What about a circle? Is that not a function? If not, why?
    Last edited by Paze; August 27th 2013 at 04:17 AM.
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    Forum Admin topsquark's Avatar
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    Re: Bijective, surjective, injective functions

    Quote Originally Posted by Paze View Post
    A General Function points from each member of "A" to a member of "B".

    To be a function you never have one "A" pointing to more than one "B", so one-to-many is not OK in a function (as you would have something like "f(x) = 7 or 9")

    Injective, Surjective and Bijective

    What about a circle? Is that not a function? If not, why?
    Use the vertical line test.

    -Dan
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    Senior Member Paze's Avatar
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    Re: Bijective, surjective, injective functions

    Quote Originally Posted by topsquark View Post
    Use the vertical line test.

    -Dan
    Thank you. What is the difference between the vertical and the horizontal line test?
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    Re: Bijective, surjective, injective functions

    Quote Originally Posted by Paze View Post
    Thank you. What is the difference between the vertical and the horizontal line test?
    Learn the actual definition of function.
    The statement that f:A\to B is a function from A to B means:
    \\ \bullet~f\subset A\times B \\ \bullet~A=\text{Dom}(f)\\ \bullet~\text{no two pairs in }f\text{ have the same first term.} That last bullet-point is the vertical line test.

    Here are some special properties of some functions.
    If \text{Img}(f)=B then the function is surjective.

    If \text{no two pairs in }f\text{ have the same second term.}  then the function is injective.( that is also known as the horizontal line test.)
    Thanks from topsquark and johng
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