Re: Motion 31 draft text V04.4, extra notes

[Vincent Lefevre <vincent@xxxxxxxxxx>]

On 2012-04-11 11:47:19 -0500, Nate Hayes wrote:
> Nate Hayes wrote:
> >>>>>When restricted to bounded intervals, the Level 1 arithmetic is
> >>>>>closed and cancellative for addition, subtraction, multiplication
> >>>>>and division with 0 not in the denominator.
> >>>>
> >>>>This is not the definition of a closed arithmetic. If you can get
> >>>>an interval as a result, say [0,1], you mustn't remove it from the
> >>>>possible inputs of an operation.
> >>>
> >>>At Level 2 its not.
> >>
> >>Do you mean that you have an operation at Level 2 with no
> >>corresponding operation at Level 1? This doesn't make sense.
> >Sure it does.
> >It all depends on the underlying axioms and definitions.
> 
> BTW, in the current P1788 model, the midpoint operation is a prefect
> example of this because it is not defined at Level 1!

Not a good example:

1. My preferred choice is to make it also undefined at Level 2 (NaN)
on the cases it is undefined at Level 1.

2. The midpoint function doesn't return an interval, meaning that
the Level 2 result can be inexact, even when it is perfectly defined
at Level 1. So, the user need to know that there are significant
differences with Level 1 in many cases.

-- 
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)