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Math Help - Real Slice of Mandelbrot set

  1. #1
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    Real Slice of Mandelbrot set

    I'm trying to prove that the real slice of a Mandelbrot set is M n R =[-2,1/4]

    I've tried researching it on the internet but everything I find seems to just state this and not prove it.
    The hint I've been given to start is is to let

    c$\in$(1/4, $\infty$) proving that for each $z$$\in$R that f$_{\text{c}}$(z)-z $\geq$ c -1/4

    where f$_{\text{c}}$(z)= z^2+c

    Any help would be greatly appreciated
    Last edited by klw289; September 1st 2012 at 12:15 PM. Reason: Mistype on first line
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  2. #2
    MHF Contributor

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    Re: Real Slice of Mandelbrot set

    What you have written makes no sense. For any real number c, fc(z)- z is a complex number. You cannot say it is "larger than c- 1/4, a real number.

    Perhaps you meant \left|f_c(z)- z\right|\ge c- \frac{1}{4}?
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