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Groups > comp.soft-sys.math.mathematica > #1921

Re: Limit[f[x], x->a] vs. f[a]. When are they equal?

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On Apr 29, 5:29 am, Richard Fateman <fate...@eecs.berkeley.edu> wrote:
> On 4/28/2011 1:30 AM, Andrzej Kozlowski wrote:

> >   In fact I once suggested that an options should be available for the user to decide which compatification he wants to use when taking limits etc,
>
> Sounds plausible to me.
>>   but now I think that this additional functionality would almost never be used and thus is not worth the effort.
> to require the user
> to check something that the system could check is to say, in effect, we
> could make Mathematica do mathematics correctly, but we will settle for
> it doing mathematics "pretty well" and in particular, sometimes wrong.

One difficulty here is that few Mathematica users would understand how
to navigate the maze, if that was the general approach. The issue
you've identified is only one in a huge set of potential "mathematical
context" issues that one might address. Like essentially everyone who
applies mathematics, you yourself throw around terms like "integral",
"function", "neighborhood", "(in)finite", "continuous", and
"differentiable" without stating the precise mathematical context in
which you are speaking. It would be a huge burden to do so, even for
the small minority who really understand these issues.

As for mathematical correctness, well, there exist computer proof
verification systems. They are much more limited in scope, and much
harder to use than Mathematica. Mathematica is more focused on
applications. Usually, the "application context" is stricter
discipline anyway. There is no guarantee that a well-formed
mathematical expression or a formally correct mathematical result
makes physical sense. Nor, in this case, have you identified a result
that is actually incorrect: you merely found a case where you got
different answers to different questions.

> Or perhaps we really don't know how to do this correctly, and we should
> just say (as I've suggested a day or two ago) that it be documented.

The documentation is already impenetrable, and it should not assume
the additional burden of providing a graduate-level education in
mathematics to Mathematica users. Mathematica relates well to the
common practice of applied mathematics education, where this kind of
mathematical context issue is not covered in any great detail. It
would be too distracting.

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Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-04-26 10:51 +0000
  Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Noqsi <noqsiaerospace@gmail.com> - 2011-04-30 09:51 +0000
    Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Richard Fateman <fateman@cs.berkeley.edu> - 2011-05-02 10:51 +0000
  Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Richard Fateman <fateman@cs.berkeley.edu> - 2011-04-28 10:35 +0000
  Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-04-28 10:36 +0000
  Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Richard Fateman <fateman@eecs.berkeley.edu> - 2011-04-29 11:29 +0000

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