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MathGroup Archive 2001

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Re: Limit question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31568] Re: Limit question
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Wed, 14 Nov 2001 03:41:43 -0500 (EST)
  • References: <9sge8a$935$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Otto Linsuain <linsuain at andrew.cmu.edu> wrote:
[snip]
> Mathematica outputs ComplexInfinity when it encounters a divergence with
> unclear phase. But what about the cases where the limits depend on the
> direction  but are not divergent, like it is 0 from the left, 1 from the
> right, 1/2 from above, etc? What should the output be then?

All questions, with the exception of the above, seem to have been well
discussed in this thread.

Here's my answer for what the output should be in such a case:
  Interval[{0,0},{1/2,1/2},{1,1},etc.]

Before reacting too strongly against this suggestion, please consider
that it is based on the same idea (good, in my opinion) which allows
Mathematica to give Interval[{-1,1}] for Limit[Sin[x],x->Infinity].

Consider then Limit[Floor[Sin[x]],x->Infinity]. By the same logic,
Mathematica should (but doesn't) give Interval[{-1,-1},{0,0},{1,1}]
or something equivalent to it.

Regards,
  David Cantrell




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