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.