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Re: Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg69693] Re: Inequalities
• From: dimmechan at yahoo.com
• Date: Thu, 21 Sep 2006 07:29:15 -0400 (EDT)
• References: <eeqpop$oe3$1@smc.vnet.net>

Hi.

You can Reduce
(http://documents.wolfram.com/mathematica/functions/Reduce)

Reduce[p*(1 - p) < q*(1 - q) && 0 < p < q < 1, {p, q}]
0 < p < 1/2 && p < q < 1 - p

There is also the package InequalitySolve
(http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Algebra/InequalitySolve.html)

InequalitySolve[p*(1 - p) - q*(1 - q) > 0 && 0 < p < q < 1, {p, q}]
(Inequality[0, Less, p, LessEqual, 1/2] && 1 - p < q < 1) || (1/2 < p <
1 && p < q < 1)

Dimitris Anagnostou




Î?/Î? misha έγÏ?αÏ?ε:
> 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!