Re: limits

*To*: mathgroup at smc.vnet.net*Subject*: [mg25608] Re: [mg25602] limits*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Mon, 16 Oct 2000 03:04:35 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Personally I think you are quite right and it is an inconsistency. Strictly speaking Limit[1/(x - 2), x -> 2] can be said to exist only when 1/(x - 2) is viewed as a complex meromorphic function (or a holomorphic mapping from the Riemann sphere to itself) but then the value at x=2 ought to be ComplexInfinity and not DirectedInfinity[1] which is what Mathematica gives. I would consider this not so much a bug as a mathematical (or even logical) mistake. Andrzej -- Andrzej Kozlowski Toyama International University, JAPAN For Mathematica related links and resources try: <http://www.sstreams.com/Mathematica/> on 00.10.11 4:50 PM, Tom De Vries at tdevries at mail2.westworld.ca wrote: > Hello all, > > Forgive the simple questions here. I'm a high school mathematics teacher > having a go at teaching calculus so my knowledge is limited. Our class is > using Mathematica and I was wondering about the interpretation of limits > using Mathematica. > > Limit[1/(x - 2), x -> 2] > > gives me an answer of infinity. However, taking the limit from both > directions shows that the limit is different coming from either side of 2. > > Limit[1/(x - 2), x -> 2, Direction -> 1] > > Limit[1/(x - 2), x -> 2, Direction -> -1] > > > When I ask Mathematica to take a limit at 2, should I not expect it to give > me an answer that would indicate that the limit does not exist since it is > different coming from above and below? > > Thanks for any help you might provide! > > Sincerely, > > Tom De Vries > Edmonton, Alberta > Canada > >