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
>

```

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