Re: Applying Mathematica to practical problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg130989] Re: Applying Mathematica to practical problems*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Sat, 1 Jun 2013 06:27:28 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <kmngb2$3rv$1@smc.vnet.net> <20130519095011.606CD6A14@smc.vnet.net> <20130530101525.2281869F1@smc.vnet.net> <ko9ipa$kde$1@smc.vnet.net>

On 5/31/2013 12:16 AM, Andrzej Kozlowski wrote: > Excuse me? I have always assumed that every number system has at least > one finite number x such that x+1=x, this follows from the group > axiom. Also, by the way, if we are talking about group addition then > "x ==0 and x+1 == x" is a not very economical way to express > x==0. I think that Andrzej is misreading/ miswriting... It is fine to have an element x such that x+1=1. That number is the identity under addition, or zero. It is not ok to have an element such that x+1=x. (When x and 1 are supposed to be modeling the real numbers). As for the rest of the attacks... z = 1.11111111111111111111;While[(z = 2*z - z) != 0, Print[z]] Well, see it for yourself (in Mathematica 9) and decide if anyone would find it so confusing. Mathematica 9 has adopted my suggestion that numbers with no precision be displayed differently (in a red box). Prior versions (up to 7 or 8?) just displayed 0. Andrzej misconstrues my comments principally in the sense that he assumes I think it is OK to have a design that gives naive users wrong answers if it is possible for a skilled user to bypass the potential disasters by switching arithmetic (etc.) No, it is a bad design. The rest of Andrzej's comments are, I think not worth responding to.