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
>
>
>
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