Re: Zero does not Equal Zero is a feature

*To*: mathgroup at smc.vnet.net*Subject*: [mg31443] Re: Zero does not Equal Zero is a feature*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Wed, 7 Nov 2001 05:29:00 -0500 (EST)*Organization*: University of California, Berkeley*References*: <9rdg39$7ob$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

These difficulties have been in Mathematica since its first design, and although there have been a number of redesigns of the arithmetic, it retains the element of treating floating point numbers as though they were intervals. Careful numerical analysis is hindered by this design, which was intended to be used by non-careful sloppy people. But the design has some flaws which make it necessary for people who know what they are doing, to re-learn a new and not very comfortable calculus of numbers, at least if they want to use Mathematica. It also interferes with sloppy calculation. One choice of course is not to use Mathematica for numerical calculation. There are other arbitrary precision packages. Another choice is to test, and reset the accuracy of numbers at critical points. Realize, for example, that certain convergent iterations will not produce more accurate answers (as is normal), but will produce vaguer answers at each step because of Mathematica's arithmetic. They will terminate not when answers are close, but when they are essentially unknown. You could also complain about the arithmetic, but that will probably not have much effect. It is a "feature". My (1982) review of Mathematica made some of the same observations. Richard Fateman www.cs.berkeley.edu/~fateman

**Follow-Ups**:**Re: Re: Zero does not Equal Zero is a feature***From:*Daniel Lichtblau <danl@wolfram.com>