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MathGroup Archive 2006

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Re: Inequalities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69699] Re: Inequalities
  • From: "Dana DeLouis" <dana.del at gmail.com>
  • Date: Thu, 21 Sep 2006 07:29:28 -0400 (EDT)

>It should be, if 1 - q > p.

Hello.  Reduce seems to suggest there are two areas.

equ = p*(1 - p) < q*(1 - q); 

FullSimplify[Assuming[0 < p < q < 1, Reduce[equ, {p, q}]]]

(p > 1/2 && p + q > 1 && p > q) || (p < 1/2 && p + q < 1 && p < q)

I wasn't sure about the 1/2 part.
However, the plot below seems to suggest it is correct.
If I'm not mistaken, the white area represents "True."

 ContourPlot[Boole[equ], {p, -3, 3}, {q, -3, 3}, Contours -> 1, 
   Axes -> True, PlotPoints -> 300, RotateLabel -> False, 
   FrameLabel -> {"\n p", "q"}, PlotLabel -> 
    "\n White Area is True \n"];

HTH
Dana DeLouis
Mathematica 5.2
dana.del at gmail.com


>I am an inexperienced user and am wondering whether Mathematica can help 
>me with inequalities such as the following.
>
>Given 0 < p < q < 1,
>
>When is p(1-p)<q(1-q)?
>
>It should be, if 1 - q > p.
>
>Thanks!


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