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

*To*: mathgroup at smc.vnet.net*Subject*: [mg109857] Re: Equals, Less, Greater, etc; Confused by this simple output.*From*: "Alexey Popkov" <lehin.p at gmail.com>*Date*: Wed, 19 May 2010 20:16:30 -0400 (EDT)*References*: <ht0gho$bn$1@smc.vnet.net>

Hello, The reason is that for complex numbers comparison operation is undefined: In[1]:= a >= a // Reduce Out[1]= a \[Element] Reals But I do not understand the reason for different outputs from Simplify and FullSimplify in such a simple case: In[1]:= Simplify[a >= a] Simplify[a >= a, a \[Element] Reals] Simplify[a >= a, a \[NotElement] Reals] FullSimplify[a >= a] Assuming[a \[Element] Reals, a >= a] Refine[a >= a] Refine[a >= a, a \[Element] Reals] Refine[a >= a, a \[NotElement] Reals] Out[1]= a >= a Out[2]= True Out[3]= True Out[4]= True Out[5]= a >= a Out[6]= a >= a Out[7]= True Out[8]= a >= a "telefunkenvf14" <rgorka at gmail.com> ÓÏÏÂÝÉÌ/ÓÏÏÂÝÉÌÁ × ÎÏ×ÏÓÔÑÈ ÓÌÅÄÕÀÝÅÅ: news:ht0gho$bn$1 at smc.vnet.net... > 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 >