Re: Motion 54: Introductory staff - signed zeros in inf-sup
John,
> My proposed solution is
>
> A. Use only one of "bound" and "endpoint". Despite Vladik's reasonable point about explaining to mathematicians,
> I prefer "bound" because, as Michel said, "endpoint" sounds as if it is always a member of the interval.
>
>
> B. Add "bound" to the Definitions. Maybe say "endpoint" is a synonym.
>
> B'. I note that §4.1 "Frequently used notation and abbreviations" needs adjustment. Should we say
F,G,... generic notation for a number format.
Yes. The next lines after B' could be
<<<<
Val(F),Val(G),... set of extended-real values of all numbers of number format.
>>>>
> Should we delete the "\overline{IF},\overline{IG}" entry as we don't use it? Or should we start using this notation systematically?
I'm for deletion of unused notation.
> I would prefer "extended-real value". How about in §12.4 "Number formats", at the end of paragraph "Following the convention of ..." add
> "The *extended-real value* (or just *value* when context makes clear)
> of an F-number is the extended-real number it denotes: namely the value
> of -0 and +0 is 0, and of each other F-number is itself."
>
> Also add this notion to the definition of a number format, 4.2.23.
Ok.
> D. In 12.5.2 change
> "The inf-sup type derived from a supported number format F ... is the bare interval type T comprising all intervals whose endpoints are in F (with
> ±0 replaced by 0), together with Empty"
> to
> "The inf-sup type derived from a supported number format F ... is the
> bare interval type T comprising all intervals whose bounds are the
> extended-real values (see §12.4) of F-numbers, together with Empty".
>
> Or, introduce new notation in 12.4, say Val(F), to mean the set of values of F-numbers. Then one could write (I prefer this):
> "The inf-sup type derived from a supported number format F ... is the
> bare interval type T comprising all intervals whose bounds are in Val(F)
> (see §12.4), together with Empty".
>
> Adjust the definition of mid-rad type similarly.
I like more Val(F).
> E. In 12.10.1, nextUp and nextDown need to be more precise. Are their input and output F-datums (as in 754 §5.3.1)?
> If so, we need to specify as 754 does that if x is the negative F-number of smallest magnitude then nextUp(x) is -0 if F contains this.
>
> I would prefer to say nextUp and nextDown are maps from Val(F) to Val(F). (They could be from extended-reals Rbar to Val(F), but is that useful?)
I also prefer map from Val(F) to Val(F).
> F. In 12.12.8 "Difficulties in implementation" could "are values of" in "In the former case, l and u are values of supported number formats ..."
> be ambiguous? Change to "belong to"?
Yes.
-Dima