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Thread: Example of a map from [-1,1] to [0,1]

  1. #1
    Newbie Throughpoint's Avatar
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    Example of a map from [-1,1] to [0,1]

    How would I find an example of such a function that maps from $\displaystyle [-1,1]$ -> $\displaystyle [0,1]$

    I was thinking.. $\displaystyle q(x)$ $\displaystyle =$
    $\displaystyle 0$ if $\displaystyle x$ is in $\displaystyle Q$
    $\displaystyle 1$ if $\displaystyle x$ is NOT in $\displaystyle Q$
    $\displaystyle x$ in $\displaystyle (0,1)$
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Throughpoint View Post
    How would I find an example of such a function that maps from $\displaystyle [-1,1]$ -> $\displaystyle [0,1]$

    I was thinking.. $\displaystyle q(x)$ $\displaystyle =$
    $\displaystyle 0$ if $\displaystyle x$ is in $\displaystyle Q$
    $\displaystyle 1$ if $\displaystyle x$ is NOT in $\displaystyle Q$
    $\displaystyle x$ in $\displaystyle (0,1)$
    How about $\displaystyle \displaystyle q(x) = \frac 1{\pi} \cos^{-1} (x)$ ?

    you're function maps to only two elements in [0,1], what a waste and x in (0,1) won't work, you must use up all elements in your domain
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  3. #3
    Newbie Throughpoint's Avatar
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    Does that map closed sets to closet sets? I need to find a function that doesn't. =/

    Thanks for your help though
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  4. #4
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    Hello, Throughpoint!

    $\displaystyle \text{How would I find a function that maps from }[-1,1]\:\to\:[0,1]\,?$

    One such function is: .$\displaystyle q(x) \,=\,x^2$
    . . This maps two points of the domain onto one point of the range,
    . . with the sole exception $\displaystyle x = 0.$

    If a one-to-one mapping is desired, try: .$\displaystyle q(x) \:=\:\dfrac{x+1}{2}$
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Throughpoint View Post
    Does that map closed sets to closet sets? I need to find a function that doesn't. =/

    Thanks for your help though
    i don't see what you mean? you did ask to map a closed set to a closed set didn't you?
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  6. #6
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    Quote Originally Posted by Throughpoint View Post
    Does that map closed sets to closet sets? I need to find a function that doesn't. =/

    Thanks for your help though
    You originally asked for a function that maps [0, 1] to [-1, 1]. Are you now telling us that that is NOT what you want to do?

    So what is your question?
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