Re: Equals, Less, Greater, etc; Confused by this simple output.

*To*: mathgroup at smc.vnet.net*Subject*: [mg109840] Re: Equals, Less, Greater, etc; Confused by this simple output.*From*: Simon <simonjtyler at gmail.com>*Date*: Wed, 19 May 2010 20:13:25 -0400 (EDT)*References*: <ht0gho$bn$1@smc.vnet.net>

Hi RG, The default assumption mathematica makes is that an unknown symbol represents a complex number, which are not ordered. Thus, while a==a is automatically evaluated, to quote the help files: "Symbolic inequalities remain unevaluated, since x may not be a real number:" Interestingly a Simplify does not evaluate the inequalities but a FullSimplify is smart enough to return True/False answers. Simon On May 19, 7:03 pm, telefunkenvf14 <rgo... at gmail.com> wrote: > Can someone offer an explanation for the following output?---I'm > trying to understand why it makes sense for Mathematica to be set up > to respond like this. (Of course, feel free to point out any glaringly > obvious math examples.) > > In[1]:= {a == a, a <= a, a >= a, a < a, a > a} > > Out[1]= {True, a <= a, a >= a, a < a, a > a} > > I would have thought that a <= a and a >= a would both evaluate to > True, given that a == a does. Also, can something really be greater > than itself? Hmmm... maybe there's hope for me after all. :) > > -RG