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Math Help - One to one

  1. #1
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    One to one

    Let A be a nonempty set and let f: A-->B be a function. Prove that f is one-to-one iff there exists a function g: B-->A such that gof = 1(subA).

    Can someone please show me how this is solved.
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  2. #2
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    Quote Originally Posted by hayter221 View Post
    Let A be a nonempty set and let f: A-->B be a function. Prove that f is one-to-one iff there exists a function g: B-->A such that gof = 1(subA).
    There is a well known theorem: There is an injection from A to B iff there is a surjection from B to A.
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  3. #3
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    Are you sure, I thought it had something to do with inverses.
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  4. #4
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    Quote Originally Posted by hayter221 View Post
    Are you sure, I thought it had something to do with inverses.
    Do you understand this problem?
    What I posted is all about 'inverses'!
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