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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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