Date: Jun 1, 2013 6:07 AM
Author: Richard Fateman
Subject: Re: Applying Mathematica to practical problems

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.