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Re: Structured support for both standard and modal intervals

Thanks, John.

I only have one further comment (see below).


John Pryce write:

Nate Hayes wrote:

P1788 already voted that the midpoint of an unbounded interval is
undefined.
So if P1788 decides there will be no overflow, then these are my
lingering
and unanswered questions:

 1. If arithmetic mean (midpoint) of an unbounded interval is undefined
at Level 1, does this mean other interval bisection methods such as
geometric mean, smedian2, etc. are also undefined at Level 1 for
unbounded
intervals?


IMO it's right that "midpoint" should be defined entirely "by the
mathematics", so undefined...

My view of undefinedness. The Hack-Neumaier flmedian is inherently
undefined at Level 1. The Pryce-Zuras smedian at Level 1 is undefined, or
infinite, for unbounded intervals. Who cares? They may be found
pragmatically useful at Level 2.


...

 3. If answer to (1) is "yes", then are all of these interval bisection
methods undefined for unbounded intervals at Level 2, as well?


For me this a matter of mathematical honesty. If ANY numeric function is
mathematically undefined for some input then say so, at Level 1; and let
it return NaN at Level 2...


 5. If answer to (3) is "yes", it seems users will not be able to write
any interval bisection methods of thier own that will be conforming,
since
picking arbitrary real number will be against the Level 1 and Level 2
definitions. So how can any user develop conforming algorithms that
bisect
unbounded intervals?


If you CALL IT SOMETHING DIFFERENT, you can make your pragmatic function
do whatever is useful. So no contradiction...
I should probably add to the Level 1 text, that other operations may be
defined at lower levels for purely pragmatic reasons.


My only problem with this idea is it means users can no longer design
interval algorithms (or prove them correct) at Level 1, and we feel it encourages users to ignore the Level 1 definitions. We believe overflow avoids this problem by providing the necessary mathematical framework at Level 1a. 

Nate