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

The Mathematica type Real is NOT a subset of the mathematical field Reals. 
Those are quit different things.
On the other hand, the Mathematica domain Reals is intended to mimic all 
properties of the mathematics Reals field.

The same is tru for Complex/Complexes.

The Mathematica Real type is CS stuff (for programming as Andrzej said). It 
represents an approximate (real) number.
Approximate real numbers, as defined in Mathematica, are "intervals" [x - 
d/2,  x + d/2] and NOT "points" on a
(infinite) number line. That fact is used in the (significance) arithmetic 
of Real numbers which is different than the arithmetic
used for real numbers.

The name Float could also been used instead of Real and would maybe be a 
better alternative.

I'm not a Mathematician as you two guys, so I could be wrong  :-)

Greetings from Croatia,

"Richard Fateman" <fateman at> wrote in message 
news:cv9af3$l1s$1 at
> 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.

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