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