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*References*: <00ed01c512b0$2f242850$6400a8c0@Main> <curpbn$r28$1@smc.vnet.net> <200502150438.XAA29728@smc.vnet.net> <200502161936.OAA19223@smc.vnet.net> <bc260b75189ab899a75c3a5c65dc0bcf@gmail.com> <4214B60F.2050207@math.umass.edu> <7264774360d595ba92f3e713df810465@mimuw.edu.pl> <cv6ru9$6jj$1@smc.vnet.net> <42177C45.5090205@cs.berkeley.edu> <a5427d79c9fda3403abd8d2423f334e0@mimuw.edu.pl>*Sender*: owner-wri-mathgroup at wolfram.com

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>