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MathGroup Archive 2003

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Re: Re: Limits: Is there something I'm missing Here?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39409] Re: [mg39390] Re: Limits: Is there something I'm missing Here?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 14 Feb 2003 03:19:39 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I once argued rather fervently the same point in the same forum but a 
message from Daniel Lichblau persuaded me I was wrong.
Briefly, the point is that Mathematica is a practical tool whose 
purpose is to what is computationally useful. It may give one a warm 
feeling of satisfaction when it returns an answer one knows already to 
be true (or quite often agrees with one's preferred mathematical 
interpretation) but if it serves no further useful purpose (meaning 
letting you compute something you did not know before you started) then 
it is better not to bother to implement it. By the way, if you load in 
the Calculus`Limit` package and evaluate the same limit you will get 
the answer you want. This feels nice, but the problem is, however, that 
it is difficult to think of how this answer could be really useful.

In the case of limits, omnidirectional limits are, in most cases when 
they can be computed at all, much more reliably computed using Series. 
Limit is mostly in precisely the cases when Series can't be used.

However, we also agreed then that the fact that Limit assumes a default 
direction definitely ought to be documented. At that time version 4.1 
was still the current one so I take it that this was simply forgotten.

Andrzje Kozlowski

>
> And it's unfortunate IMO that Mathematica's Limit, in absence of a
> specified Direction, doesn't give the omnidirectional limit. For the
> problem at hand: If we deal with the projective extension of the 
> complexes,
> the omnidirectional limit of 1/x as x -> 0 is, truly is, 
> ComplexInfinity.
>
> David Cantrell
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/



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