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!