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.
What you want is the minimal distance between s and the set/interval
[-1,1], which is 0 if -1 ? s ? 1.
-s
On Tue, Sep 8, 2009 at 1:49 PM, Richard Fateman<fateman at cs.berkeley.edu> wrote:
> if ?y=limit(f(t),t,x) ?then as t approaches x, f(t) approaches y. But if y
> is an interval, say [-1,1], ?then f(t) never approaches y in a uniform
> sense, regardless of how close t approaches x.
> (typically x is infinite in these cases)
>
> If f(t) is a scalar s between -1 and 1, then the distance between s and
> [-1,1] is an interval of length 2, and doesn't get smaller.
> Perhaps it is possible to reinterpret the definition of limit to accommodate
> this, but I haven't seen it. ?You'd have to redefine derivatives, no?
>
> RJF
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