Exactly.
On 2010-09-13, Viktor T. Toth <vttoth at vttoth.com> wrote:
> Correct me if I am mistaken but I think a basic assumption behind
> simplification is that any unevaluated symbol represents a finite,
> determinate quantity. Hence, you're allowed to simplify 0*x as 0, even
> though 0*inf is definitely not 0, because the value of x, whatever it might
> be (real number, complex number, vector, matrix, operator, quaternion,
> etc.), is not infinite or indeterminate.
>
>
> Viktor
>
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
> On Behalf Of Stavros Macrakis
> Sent: Sunday, September 12, 2010 6:52 PM
> To: Richard Hennessy; maxima at math.utexas.edu
> Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
>
> As Fateman has pointed out on this discussion before, Maxima often
> assumes the general case, even when there are special cases which are
> incorrect. For example, Maxima simplifies x/x => 1 without the caveat
> that x # 0.
>
> As for 'limit', it tries to be careful about cases like this, and it
> does assume (sensibly I think) that independent parameters are finite.
> You make it sound very simplistic. Certainly it has bugs and
> limitations, but they're (mostly!) not quite as trivial as you're
> implying.
>
> -s
>
> On 2010-09-12, Richard Hennessy <rich.hennessy at verizon.net> wrote:
>> 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
>>>>
>>>>
>>>>
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>>>>
>>>
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>>
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