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From: telefunkenvf14 on 19 May 2010 07:03
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

From: Simon on 19 May 2010 20:11
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...(a)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


From: Raffy on 19 May 2010 20:13
On May 19, 4:03 am, telefunkenvf14 <rgo...(a)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

Equal will return true if the sides are identical (and not
Indeterminate or Overflow).

GreaterEqual, Greater, LessEqual, Less will only return true/false if
its arguments are reals.

To produce the desired result:
Block[{a}, FullSimplify[{a == a, a <= a, a >= a, a < a, a > a}]]

From: Alexey Popkov on 19 May 2010 20:14
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(a)gmail.com> �������/�������� � �������� ���������:
news:ht0gho$bn$1(a)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
>



From: ingolf.dahl on 19 May 2010 20:14
Try with these, and you will see that there is some sense in the Mathematica
output:

With[{a = "a little string"}, {a == a, a <= a, a >= a, a < a, a > a}]

With[{a = 1 + I}, {a == a, a <= a, a >= a, a < a, a > a}]

With[{a = {5, 2}}, {a == a, a <= a, a >= a, a < a, a > a}]

With[{a = (# &)}, {a == a, a <= a, a >= a, a < a, a > a}]

Best regards

Ingolf Dahl
ingolf.dahl(a)telia.com

-----Original Message-----
From: telefunkenvf14 [mailto:rgorka(a)gmail.com]
Sent: den 19 maj 2010 13:03
Subject: Equals, Less, Greater, etc; Confused by this simple
output.

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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