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