[Maxima] extending limit
macrakis at alum.mit.edu
Tue Sep 8 13:51:21 CDT 2009
I don't think the "distance from interval" application is very common,
and in fact interval operations on limitsets are meaningful in other
In particular, for continuous f, f( limitset(A), limitset(B) ) is a
subset of limitset( f(A,B)), so interval arithmetic *does* make sense
for that application.
For example, limitset( sin(x) ) - limitset (max(0,sin(x))) =
interval(-1,1) - interval(0,1) = interval(-2,1), whereas limitset
(sin(x)-max(0,sin(x))) = interval(-1,0).
On Tue, Sep 8, 2009 at 2:23 PM, Richard Fateman<fateman at cs.berkeley.edu> wrote:
> Stavros Macrakis wrote:
>> If f(t) has a well-defined, unique limit as t approaches x, then the
>> limit set of f(t) in the neighborhood of x is exactly that point.
>> If it does not have a single limit point, then the limit set is an
>> excellent characterization of its behavior in that neighborhood.
>> Calculating s-[-1,1] as an interval calculation here isn't meaningful.
> I agree. which is why I think that representing the limit set as an
> interval is hazardous, because
> once you have an interval, it has different semantics associated with it.
> If you return
> another object which is a "limit set" you might be safer. I'm not
> sure where this will really bite you. That depends on how much you actually
> do with intervals
> that come out of limit calculations. Most people do nothing with this
> information beyond
> printing it out, which is probably not going to run into problems.
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