Re: A proposal for the next motion
P1788 group
Last week I moved into my new home - actually an old house neglected for some 50 years, where life will consist of "camping" for several months while needed modernisations are done. But at last I have time to get back to interval matters.
Arnold Neumaier's suggested wordsmithing group seems a good idea to me if some people want to do it as a voluntary task, rather than as a formal procedure of P1788.
Arnold points out slips and makes several suggestions for improved language that I agree with, see below. I will shortly re-issue M0005 amended as he suggests, and will respond, in separate emails, to other comments by him and others.
My text is not a hodge-podge of disparate ideas as someone said, but a unified linear development. If at some point you disagree with my view, then your line deviates from mine at that point, and the rest of my line may seem irrelevant to you.
These points of deviation reveal various controversial issues, each of which is likely to need its own motion, discussion and vote.
Regards
John
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Arnold's points that I agree with:
> I object to calling the transcendental function exp(xx) an algebraic function.
> I propose to differentiate between an interval *function*, which is
> an interval extension of a real function, and an interval *mapping*,
> which is a mapping between interval spaces.
A good terminology idea. Thanks.
> ''smallest'' --> ''tightest''
In most mathematics where sets are used, ''smallest'' is the more common usage for "a set which, among those sets having a certain property, is a subset of all the others". I'll clarify, and may adopt ''tightest'' since it is popular in interval literature.
> (1) has already a meaning in this document
Yes, I used (1), (2), ... ambiguously, as clause numbers and as equation numbers. Thanks.
>> that is if at least one argument is NaI -- then, by definition, the result is NaI.
> By which definition? Or is _this_ the definition?
It is. I'll clarify.
> Probably: ''_an_ interval evaluation'', not _the_, since the nature of
> ee_F is not specified.
Yes. My notation does have some inconsistency here.