Re: How do I bisect unbounded intervals?

[John Pryce <j.d.pryce@xxxxxxxxxxxx>]

Dan, Vincent, Nate etc.

This discussion reminds me of a Level 2 issue that must be resolved. When discussing finite precision it's clear you've all been assuming an inf-sup representation. How do midpoint and the other numeric functions of intervals work for an _implicit_ type?

I've basically defined an interval type T as a set of mathematical intervals plus a specified T-hull operation. No number-format is mentioned. But Level 2 midpoint, etc., must return a datum of some number format. Hence I see nothing for it but to make the revised definition:

   An interval type T is a set of mathematical intervals,
   plus a specified T-hull operation, plus a specified
   number format, let's call it the T-format.

For each implemented T, each numeric operation on intervals shall have a T-version that returns a result of this T-format. (One might allow different operations to return results of different formats, but to me that seems way too complicated.)

Your views please. Any further complications (Ugh!) that need to be made?

I'll comment on the midpoint/bisect discussion separately.

John Pryce