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MathGroup Archive 2001

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Re: Re: Limit question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31528] Re: Re: Limit question
  • From: Otto Linsuain <linsuain at andrew.cmu.edu>
  • Date: Fri, 9 Nov 2001 06:13:33 -0500 (EST)
  • Approved: Steven M. Christensen <steve@smc.vnet.net>, Moderator
  • Sender: owner-wri-mathgroup at wolfram.com

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.

On Thu, 8 Nov 2001, Erk Jensen wrote:

>
> Why not? What's wrong with that?
> If you don't specify the direction, why should it assume that you want the
> limit from the left?
>
> Why is Limit[1/x,x->0] = infinity? Shouldn't that by your logic be -infinity?
>
> Your solution obivously is to specify the direction!
>
> Ciao
>   -erk-
>
>



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