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

• To: mathgroup at smc.vnet.net
• Subject: [mg54443] Re: Bug Report - Two numerical values for a same variable
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sun, 20 Feb 2005 00:10:34 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote:

> 
> On 19 Feb 2005, at 20:54, Richard Fateman wrote:
> 
>> 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.
>>
> Well, if you really know any people who think that computer programs 
> "understand" anything than you move in curious circles. But just a 
> moment, who was it who 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.
>>
> Understands?
> 
> Andrzej Kozlowski
> 


I quote from you, "Mathematica certianly undersands Reals,"

by which I believe you intend for us to believe that Mathematica
understands the concept of real numbers in mathematics.

If you mean Mathematica has a heuristic program that is intended to figure
out if an expression is guaranteed to be mathematically real, then
But it is not a decision procedure to determine membership.
   If that is what you meant by "understands", I don't disagree.

When I said Mathematica only understands Real, I meant the PROGRAM
named "Real" is part of Mathematica, and it is an executable constructor
for a data type.  The possibilities for encoding data as object
with Head Real constitute a subset of the mathematical real numbers.

While anthropomorphizing  has its dangers, I think these two
examples are different.

RJF