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Math Help - injection, surjection and bijection questions

  1. #1
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    injection, surjection and bijection questions

    f, g : N -> N (Natural Numbers including zero)

    f is injective but not surjective
    g is surjective but not injective

    1) Is it possible for (f composit g) to be a bijection?
    2) Is it possible for (g composit f) to be a bijection?
    3) Would the answers 1) and 2) be different if the natural numbers did not include zero?


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  2. #2
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    Quote Originally Posted by pseudonym View Post
    f, g : N -> N (Natural Numbers including zero)
    f is injective but not surjective
    g is surjective but not injective
    1) Is it possible for (f composit g) to be a bijection?
    2) Is it possible for (g composit f) to be a bijection?
    3) Would the answers 1) and 2) be different if the natural numbers did not include zero?
    The answers are:
    1) NO
    2) YES
    3) NO

    For #2 think about the floor function.
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