I get using real number mathematics that 0*x = 0 for all x. I get from extended real arithmetic that und*0 # 0 or inf*0
# 0. So I can prove that the answer is both zero and nonzero at the same time depending on the approach. So extended
real arithmetic is not self consistent.
FWIW.
--------------------------------------------------
From: "Richard Hennessy" <rich.hennessy at verizon.net>
Sent: Saturday, September 11, 2010 11:16 PM
To: "Richard Fateman" <fateman at cs.berkeley.edu>
Cc: "Maxima List" <maxima at math.utexas.edu>
Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
> Rich,
>
> I have been reading your paper, there is more to this than I thought. I have not finished reading the paper yet, it
> is a lot to digest. I would have been satisfied with not allowing arithmetic on inf, minf, und or ind. I suppose that
> is not good enough.
>
> Rich
>
>
> --------------------------------------------------
> From: "Richard Fateman" <fateman at cs.berkeley.edu>
> Sent: Saturday, September 11, 2010 10:07 AM
> To: "Leo Butler" <l.butler at ed.ac.uk>
> Cc: <maxima at math.utexas.edu>; "Andreas Eder" <andreas_eder at gmx.net>
> Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
>
>> At the risk of repeating myself, I can refer you to a paper that suggests this fits within
>> a framework of interval arithmetic.
>> e.g. interval(-inf, inf) means --- there is a real number but we don't know anything about its value.
>> this is perhaps indefinite (IND)
>>
>> an empty interval (we can choose one to be canonical) that has nothing in its interior means
>> --- there is no number that this could be, which is perhaps undefined (UND)
>>
>> http://www.cs.berkeley.edu/~fateman/papers/interval.pdf
>>
>> There are what I consider misuses of intervals regarding limits that are present in Mathematica and Maple,
>> eg..
>>
>> limit(sin(x),x,inf) ?=? interval(-1,1).
>>
>> This leads to either erroneous answers to limit problems and things related to limits, or to a substantially
>> overloaded notion of "equality". Like any interval that contains 0 is equal to 0.
>>
>> Whether this can be put together in a computer algebra system to be more consistent is possible, but
>> consistency in general is tough, and certainly not achieved now.
>> There are many examples in which, for some procedure f,
>>
>> f(a) is different from subst(a,x, simplify(f(x)) )
>> where x is some arbitrary symbol and a is some particular value.
>>
>>
>> RJF
>>
>>
>>
>> _______________________________________________
>> Maxima mailing list
>> Maxima at math.utexas.edu
>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>
>
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>