Re: Unbounded intervals
Nate,
I really do not understand the discussion about unbounded intervals.
I thought they were accepted with motion 3
A few points:
-- No computer (that I'm aware of) can numerically prove hardly
anything
useful about the domain of a function beyond the underlying numeric
limits
of the system;
Are you denying that we all support interval arithmetic in order to be
able to prove mathematical facts on a computer?
or where is the misunderstanding
| so for this reason alone, truly unbounded intervals are never
| necessary in numeric models or computations
but they are helpful and convenient
in the interval Newton method, e.g. unbounded intervals are generated by
division or reverse multiplication
Since they are used in a partition of the reals they can not be replaced
by some family of overflow thresholds
-- An overflown interval [1,+OVR] := { [1,a] | a >= H_f }, where
H_f is
a parameterization of any would-be Level 2 format, is functionally
equivalent to an unbounded interval but retains a notion of the "largest
representable number"; for this reason it is possible to define
midpoint([1,+OVR]) at Level 1 in the same way P1788 is currently
considering
to do so at Level 2.
I share Vincent's comments
-- Replacing "midpoint" with "any member of the interval" gives a
valid
mathematical definition of the Interval Newton, but such a definition is
also then no longer an algorithm because the exact method of choosing
"any
member of the interval" is left undefined.
again I agree with Vincent
Juergen
-- - Prof. Dr. Juergen Wolff von Gudenberg o Lehrstuhl fuer Informatik
II / \ Universitaet Wuerzburg, Am Hubland, D-97074 Wuerzburg InfoII o
Tel.: +49 931 / 31 86602 Fax ../31 86603 / \ Uni
E-Mail:wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx o o Wuerzburg