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MathGroup Archive 2001

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Re: Re: Limit question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31529] Re: Re: Limit question
  • From: Erk Jensen <Erk.Jensen at cern.ch>
  • Date: Fri, 9 Nov 2001 06:13:34 -0500 (EST)
  • Approved: Steven M. Christensen <steve@smc.vnet.net>, Moderator
  • Organization: CERN http://www.cern.ch
  • References: <Pine.GSO.4.33L-022.0111080931100.2837-100000@blackcomb.weh.andrew.cmu.edu>
  • Sender: owner-wri-mathgroup at wolfram.com

Otto Linsuain wrote:
> 
> Well Erk, there is something wrong with that. It is misleading! If the
> Limit is not independent of the direction, then, strictly speaking, the
> Limit does not exist. Mathematica should not give you a value for the
> Limit in that case unless you specify the Direction. Or it should at least
> specify under what conditions you get what limit. For example, when you
> ask Mathematica for an integral that depends on some parameters it might
> give you a conditional answer, something like
> 
> If[parameters satisfy some condition, one answer, another answer]
> 
> With the Limit function, this is complicated because there is a continuum
> of possible directions on the complex plane. If it was just
> Direction -> -1 or +1, then I am sure the fellows at Wolfram would have
> solved this long ago.
> 
> As for the limits Limit[1/x, x->0] and Limit[Tan[x],x->Pi/2], without
> specifying a direction, the correct answer is that they don't exist.
> 
> Otto Linsuain.

Thanks a lot for your many comments, I got the point. 

I understand that Direction->Automatic actually takes Direction->-1. This
explains Mathematica's behaviour.

So in your opinion, should then Limit[1/x,x->0] remain unevaluated by default? 
Or what doyou think would be a reasonable answer for Direction->Automatic?

Cheers
   -erk-


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