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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)
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*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.
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