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Math Help - proof

  1. #1
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    proof

    Show that |R|=|(-1,1)|. Hint consider the function f: R-->(-1,1) defined by f(x)=x/|x|+1.
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  2. #2
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    Quote Originally Posted by natewalker205 View Post
    Show that |R|=|(-1,1)|. Hint consider the function f: R-->(-1,1) defined by f(x)=x/|x|+1.
    You have to just show f is bijective.Where are you stuck?

    1) Show f(x)=f(y) \Rightarrow x=y

    2) Show \forall y \in (-1,1), \exists x \in \mathbb{R}:f(x)=y
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