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

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On 4/28/2011 1:30 AM, Andrzej Kozlowski wrote:
>
> ...
>> RJF said:
>> So the idea of a limit as x->x0  makes no sense if x0 is a member of some set of numbers, symbols, whatever.  Maybe the documentation for Limit should provide some information on this?
>>
>>
>
> AK said:
> Although these two compactifications are not compatible,

So you agree with me.
> there is no reason why they should be any more confusing to an informed user than the ability to add strings to numbers is.
Note, however,  that "string" and "number" are different types with 
different Heads.  ComplexInfinity and Infinity have the same Heads.
Neither of these infinities though, is NumberQ.  Which may sometimes be 
a good idea, depending.



>   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.
I hardly ever use the emergency blinker in my car. Maybe I should have it removed.

>   In my opinion things work pretty well as there are now (barring bugs and user ignorance, both of which are fundamental "facts of life").
There is no way to legislate against ignorance.  But 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.

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. For 
example we could specify that Limit computes the real-valued limit of a 
real-valued function at a real-valued limit point approached from a 
real-valued direction in a continuous fashion.   We could, starting with 
that, allow (real positive) infinity, and consequently also its negative.


> Andrzej Kozlowski
>
>

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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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