Re: P1788: PLEASE VOTE: M0013.04 & M0020.01
Am 02.10.2010 18:17, schrieb Arnold Neumaier:
Corliss, George wrote:
Voting on Motion M0013.04 Comparison Relations ends on Friday,
October 8.
Current count: Yes: 13; No: 0; Required for quorum: 37
Voting on Motion M0020.01 Comparison Relations ends on Friday,
October 8.
Current count: Yes: 10; No: 2; Required for quorum: 37
The complexity pmomoted in these motions is not warranted by the
applications. After having challenged the use of these relations,
not a single application was pointed out.
This is not correct. Applications using <= were mentionend in a mail by
Juergen Wolff von Gudenberg.
Other comparisons were also mentioned to be needed by other mails.
The <= relation is the connection link between the set definition of the
arithmetic operations for intervals and the explicit formulas for
computing the result of the operations by the bounds of the operands,
not just for real intervals but also for real interval vectors and
interval matrices and again for complex intervals and for complex
interval vectors and matrices.
For the <= relation compatibility relations hold between the algebraic
structure and the order stucture similar to the real numbers.. For
instance:
1. If a <= b ==> a + c = b + c for all c. 2. If a <= b ==> -b <= -a. 3.
If 0 <= a <= b and c >= 0 ==> ac <= bc and ca <= cb. Similar for division.
Ulrich Kulisch
Arnold Neumaier
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Karlsruher Institut für Technologie (KIT)
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Prof. Ulrich Kulisch
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