       Re: Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg69774] Re: Inequalities
• From: "Dana DeLouis" <dana.del at gmail.com>
• Date: Sat, 23 Sep 2006 04:43:45 -0400 (EDT)

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

Well, could I have messed that up any more?

I just realized that Assuming in this context didn't work because Reduce
doesn't have the option 'Assumptions'.
This appears to describe the area a little better.

equ = p*(1 - p) < q*(1 - q) && 0 < p < q < 1;
sol = FullSimplify[Reduce[equ, {p, q}]]

0 < p < 1/2 && p < q && p + q < 1

We see the above 3 boundaries with a quick check...

ContourPlot[Boole[equ], {p, -1, 1}, {q, -1, 2}, PlotPoints -> 200];

HTH
Dana

<snip>

>>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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