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Re: Bug Report - Two numerical values for a same variable

• To: mathgroup at smc.vnet.net
• Subject: [mg54433] Re: Bug Report - Two numerical values for a same variable
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sun, 20 Feb 2005 00:09:59 -0500 (EST)
• Organization: University of California, Berkeley
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Andrzej Kozlowski wrote:

> *This message was transferred with a trial version of CommuniGate(tm) Pro*
> On 19 Feb 2005, at 18:49, Richard Fateman wrote:
> 
>>
>> The fact that these are stand-ins for well-known mathematically real
>> quantities is irrelevant to Mathematica, since it only understands Real,
>> and Real is a subset of mathematical real.
>>
> 
> This is simply untrue in modern versions of Mathematica:
> 
> In[4]:=
> Element[Pi,Reals]
> 
> Out[4]=
> True
> 
  Check your spelling.

  Real is the Head of a floating point number.

Reals   (note the "s") at the end,  is a domain name.

Mathematica misuses the term Real which has a well-known meaning
in mathematics.

The presence of a test whereby E is known to be mathematically real
is irrelevant to the use of a data-structure-building program that
takes two numeric inputs and produces a pair of numbers. The matter
at issue is the evaluation of Complex[a,b]  not Element[??,Complexes].




> and so on. Mathematica certianly undersands Reals, 

I would not say the Mathematica  >>>understands<<< reals.

it is just that Real
> an Reals, Complex and Complexes, Rational and Rationals play different 
> roles. The former are somewhat akin to types in other languages

Yes, and that (former) is what was being discussed.

  and are
> usued basically for programming the latter are used for mathematics. 

No, it is not mathematics. It is symbolic manipulation.  That is why
(1-Sqrt[z])*(1+Sqrt[z])-z  is not known to be Real.  (neither True nor False).
Simplify,  a symbolic manipulation procedure, helps.  In mathematics,
the truth of the statement does not depend on applying procedures like
Simplify.

I
> find it perfectly satisfactory, knowing your opinions I am sure you 
> don't but that is all this amounts to and nothing one can argue about.

I suspect that Mathematica's routines for testing for membership in
domains like Reals etc.  are pretty good.  I don't, however, expect it
to understand anything. Just symbolic manipulation.  That's different.

> 
> 
> Andrzej Kozlowski
> 

• References:
  • Re: Bug Report - Two numerical values for a same variable
    • From: Scott Hemphill <hemphill@hemphills.net>
  • Re: Re: Bug Report - Two numerical values for a same variable
    • From: Murray Eisenberg <murray@math.umass.edu>