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Math Help - does f(x) = x^2 map Z onto Z?

  1. #1
    Member pberardi's Avatar
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    does f(x) = x^2 map Z onto Z?

    I do this:
    f(x) = x^2
    y = x^2
    x = y^2
    root(x) = y Since for some y in Z there is not an x in Z, this function does not map Z onto Z.

    Am I thinking about this right? I am guessing no because isn't there some theorem that states that the set of natural numbers and the set of its squares are bijective? Doesn't this say that maps N to N? No real difference between N and Z. I need some clarification here. Thanks.
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  2. #2
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    Is there any t \in \mathbb{Z} such that t^2=-5~?
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  3. #3
    Member pberardi's Avatar
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    I clarified the range to be the set of squares. Thanks for the assistance Plato.
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  4. #4
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    Quote Originally Posted by pberardi View Post
    I clarified the range to be the set of squares.
    In the future please adjust the title also. I answered the title.
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