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