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Re: Limit[f[x], x->a] vs. f[a]. When are they equal?

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  • Subject: [mg118442] Re: Limit[f[x], x->a] vs. f[a]. When are they equal?
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Thu, 28 Apr 2011 06:35:39 -0400 (EDT)
  • References: <ip6834$bmt$1@smc.vnet.net>

On 4/26/2011 3:51 AM, Andrzej Kozlowski wrote:
.. skipped and snipped...


> and so on. In Mathematica is no sense in taking limits as z ->ComplexInfinity

> without specifying a direction as there is no natural direction.

So the idea of a limit as x->x0  makes no sense if x0 is a member of 
some set of numbers, symbols, whatever.  Maybe the documentation for 
Limit should provide some information on this?

I don't know what you have written previously on this topic and have no 
intention of looking it up.  But in a system which includes 
ComplexInfinity, a concept which unifies at one "place" positive real 
infinity and negative real infinity, it becomes tricky to also have the 
separate values +Infinity and -Infinity.

some of my thoughts are in section 4 of
http://www.cs.berkeley.edu/~fateman/papers/interval.pdf

RJF







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