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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
> 
>