Moore's new book on interval analysis
Ulrich Kulisch wrote:
(in: P1788: Our first formal motion: IR versus *IR)
I think we are talking about mathematics. If mathematics is viewed as
the science of the structures then IR as it is defined in the
StandardNotation is an incomplete entity. With respect to set inclusion
as an order relation it is an ordered set. But the empty set, for
instance, which may be the result of an intersection is excluded.
Let me mention that the brand new book
R.E. Moore, R B. Kearfott and M.J. Cloud,
Introduction to Interval Analysis,
SIAM, Philadelphia, 2009.
which I got today, treats interval arithmetic on the theoretical level
in the traditional way as the arithmetic of nonempty, closed and bounded
intervals. Division is defined only for denominators not containing zero.
Unfortunately, the book does not conform to the standard notation
paper, although both publications have one of the coauthors in common.
No special symbol is used for the set of all (Moore) intervals.
On the whole, the contents of the book is elementary and fairly
conventional. Notable about the book are
- the final Chapter 11, which references and surveys a large number
of recent application of interval techniques, and
- the use of Intlab throughout the book to illustrate the techniques.
Arnold Neumaier