Re: Motion on interval flavors
John, Nate, Alexandre, p1788
On Wed, 20 Jun 2012 10:10:23 -0500, Nate Hayes wrote
> Alexandre Goldsztejn wrote:
> > - Scientific point of view. Several experts, including me, have
> > claimed that every thing that can be done using Kaucher intervals can
> > also be done using standard intervals
>
> Folks, these claims by Alexandre are simply false.
Even if they were true it would not be a good reason to sweep out the
modal intervals.
>From a scientific point of view , it quite fruitful to use various points of
view
Macroscopic, microscopic , atomic or subatomic in Physics for example.
Similarly for a given application one approach may be more more convenient
that the others.
To insure a wide usefulness of a product a variety of approaches must be
available, keeping in mind that nobody use all of them.
However these points of view are valid in different contexts.
IMHO there are similar context difference with various interval flavors.
Namely
1) The FTIA is valid whenever the function is everywhere continuous,
only defined or even partly undefined.
2) The analog of the FTIA for modal interval requires the function used
is everywhere continuous. Furthermore the statement of theorem is
considerably more involved.
3) The analog of the FTIA for midrad intervals requires the function
is defined but not necessarily continuous.
Thus, to me, flavors do not seem to be right way to describe various interval
types. Furthermore describing all the interval types on the same footing would
be misleading and should be avoided.
My proposition is to defined first the regular ( or basic) interval first as
the main line of the standard.
The other type of interval are defined as tools grounded on regular intervals.
For example regular intervals can be used as modal but in the context of the
modal interval tools
In contrast regular interval cannot be directly used by the midrad interval tool.
Sincerely
Dominique