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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
>
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