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-