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Thread: Absolute Value

  1. #1
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    Absolute Value

    Does |x - |y-z|| = |x - y + z|?

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  2. #2
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    Re: Absolute Value

    $\displaystyle |x - |y-z|| \ne |x - y + z|$ in general. Example take $\displaystyle x=3, y=1, z=2$ then we have $\displaystyle |3 - |1-2|| = |3-(2-1)|=|3-2+1| \ne |3-1+2|$
    Can you say in general under what condition $\displaystyle |x - |y-z|| = |x - y + z|$ true?
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  3. #3
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    Re: Absolute Value

    Can it be simplified then? Basically, I trying to determine if |x - |y-z|| = ||x-y| -z|
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  4. #4
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    Re: Absolute Value

    Quote Originally Posted by jzellt View Post
    Does |x - |y-z|| = |x - y + z|?

    Thanks
    Remember that $\displaystyle \displaystyle \begin{align*} |X| = X \end{align*}$ ONLY if $\displaystyle \displaystyle \begin{align*} X \geq 0 \end{align*}$.

    Here you are wanting $\displaystyle \displaystyle \begin{align*} \left| x - |y - z| \right| = \left| x - \left( y - z \right) \right| = \left| x - y + z \right| \end{align*}$. To do this, you require $\displaystyle \displaystyle \begin{align*} y - z \geq 0 \implies y \geq z \end{align*}$.
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  5. #5
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    Re: Absolute Value

    Disregard this post. It's been a long day...
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