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

```

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