On Sat, Sep 11, 2010 at 10:07, Richard Fateman <fateman at cs.berkeley.edu>wrote:
> ...There are what I consider misuses of intervals regarding limits that are
> present in Mathematica and Maple,
> eg..
>
> limit(sin(x),x,inf) ?=? interval(-1,1).
>
> This leads to either erroneous answers to limit problems and things related
> to limits, or to a substantially
> overloaded notion of "equality". Like any interval that contains 0 is
> equal to 0.
>
The limit set of sin(x) as x goes to inf is certainly [-1,1], and as you
have pointed out many times, interval arithmetic in general gives a
*superset* of the exact result. So I see no problem with [-1,1] - [-1,1] =>
[-2,2].
It is of course silly to define [-1,1]==0; who does that? If we apply the
superset approach to relationals and booleans, [-1,1] == 0 must yield {t,f}.
So what's the problem?
-s