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Re: How can I evaluate this statement?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89931] Re: How can I evaluate this statement?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 24 Jun 2008 06:17:49 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g3q7n2$akf$1@smc.vnet.net>

pircdefense wrote:

> I'm trying to show for all real numbers whether the following statement is true or false:
> 
> If a > b, then a^2 > b^2. I've tried various syntax and configurations in Mathematica, but I can't get it to report true or false. Can anyone offer a solution?

Functions such as ForAll, Exists, Resolve, Reduce, or FindInstance are 
your friends here. For instance,

In[1]:= Resolve[ForAll[{a, b}, a > b, a^2 > b^2]]

Out[1]= False

In[2]:= Resolve[ForAll[{a, b}, Inequality[a, Greater, b, GreaterEqual, 0],
      a^2 > b^2]]

Out[2]= True

In[3]:= Reduce[a > b && a^2 > b^2]

Out[3]= (b <= 0 && a > -b) || (b > 0 && a > b)

In[4]:= FindInstance[a > b && a^2 > b^2, {a, b}]

Out[4]= {{a -> 2, b -> -1}}


Regards,
-- Jean-Marc



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