Re: Re: Limit and Abs

*To*: mathgroup at smc.vnet.net*Subject*: [mg31256] Re: [mg31230] Re: Limit and Abs*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Tue, 23 Oct 2001 04:53:35 -0400 (EDT)*References*: <200110170935.FAA19657@smc.vnet.net> <9qokm5$mt3$1@smc.vnet.net> <200110200827.EAA12201@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

I'd hate to enter an argument on this topic, but even if, as you say, "Interval[{0,1}] provides more useful information than merely saying "does not exist".", the fact remains that the definition of limit is precise. I wonder if it is true that "Mathematica has a more generalized notion of limit than is often used". If such were the case, it would be necessary to redefine established mathematical concepts, wouldn't it? Tomas ----- Original Message ----- From: "David W. Cantrell" <DWCantrell at sigmaxi.org> To: mathgroup at smc.vnet.net Subject: [mg31256] [mg31230] Re: Limit and Abs > Tomas Garza <tgarza01 at prodigy.net.mx> wrote: > > And what, may I ask, is the "correct answer"? Your function is periodic > > with period Pi. The only answer is > > > > In[1]:= > > Limit[Cot[a]/(2 + Cot[a]), a -> Infinity] > > > > Out[1]= > > Limit[Cot[a]/(2 + Cot[a]), a -> Infinity] > > > > And, unless there is a misprint in your second expression below, the > > limit with *n* -> Infinity has to remain unevaluated, because a is not > > defined. But, then, if there is a misprint and you meant a -> Infinity > > instead of n->Infinity, > > As we now know, he didn't mean either! But taking a -> Infinity does > raise an interesting point. > > > the function is again periodic with period Pi > > (look at the graphs). The limit doesn't exist, and Mathematica has no > > alternative but to leave the expression unevaluated. > > False! As others have pointed out, Mathematica does have other > alternatives, and the one it chooses, returning a limit of 1, is > incorrect. In my opinion, it should have returned Interval[{0,1}] > as the answer instead. Mathematica has a more generalized notion of > limit than is often used. For example, although most of us would > normally say simply that Limit[Sin[a], a -> Infinity] does not exist, > Mathematica gives Interval[{-1,1}]. This is correct in a sense. I have > no objection to it; indeed, it provides more useful information than > merely saying "does not exist". > > David Cantrell > > > From: "Oliver Friedrich" <oliver.friedrich at tz-mikroelektronik.de> To: mathgroup at smc.vnet.net > To: mathgroup at smc.vnet.net > > Subject: [mg31256] [mg31230] Limit and Abs > > > > > Hallo, > > > > > > if I evaluate > > > Limit[Cot[a]/(Cot[a]+2),a->Infinity] > > > i get the correct answer. > > > > > > But I want to evaluate > > > > > > Limit[Abs[Cot[a]]/(Abs[Cot[a]]+2),n->Infinity] > > > > > > and that's being returned unevaluated. > > -- > -------------------- http://NewsReader.Com/ -------------------- > Usenet Newsgroup Service >

**References**:**Limit and Abs***From:*"Oliver Friedrich" <oliver.friedrich@tz-mikroelektronik.de>

**Re: Limit and Abs***From:*"David W. Cantrell" <DWCantrell@sigmaxi.org>

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