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MathGroup Archive 2001

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Re: Limit and Abs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31258] Re: Limit and Abs
  • From: DWCantrell at aol.com
  • Date: Tue, 23 Oct 2001 04:53:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 10/22/2001 17:38:26 GMT Daylight Time, 
tgarza01 at prodigy.net.mx writes:

>  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.

The definition of limit, appropriate to the context with which we are most 
familiar, is indeed precise. And so are definitions of limit in more general 
contexts.

Note that Interval[{0,1}] is not a real number. Thus, when Mathematica says 
that this is the limit, you know that the limit, as a real number, does not 
exist. This is consistent with the simpler, more common notion of limit.

>  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?

No, because the generalization is consistent, so to speak, with the 
original, more restricted notion.

   David


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