Re: 1/[0,2]=NaI
Arnold Neumaier wrote:
> On the other hand, standard interval arithmetic is only concerned with
> the problem
> (for some x \in [0,2]) y = 1/x (**)
> Again, (*) is a y-dependent predicate. It has the value true precisely
> for all y in [1/2,inf]. Therefore, the natural interval answer to
> this query is [1/2,inf], as computed by _my_ definition of interval
> division.
Arnold, the "natural" interval answer [1.25,2] is also a valid solution to
your definition since x \in [.5,.8] represents "some" x \in [0,2]. In fact,
any interval Y \subseteq [1/2,Inf) will satisfy your definition. What you
define is essentially the inner rounding.
Nate