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Math Help - Construct an explicit bijection from (0,1) to [0,1]

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    Construct an explicit bijection from (0,1) to [0,1]

    Construct an explicit bijection from the open interval (0,1) to the closed interval [0,1].
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  2. #2
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    Quote Originally Posted by qtpipi View Post

    Construct an explicit bijection from the open interval (0,1) to the closed interval [0,1].
    how about this: f(x) = \begin{cases} 0 & x = \frac{1}{2} \\ \frac{1}{n-2} & x =\frac{1}{n} , \ n \geq 3, \ n \in \mathbb{N} \\ x & \text{otherwise} \end{cases}.
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