Re: motion elementary functions
Dan, P1788
On 19 Oct 2009, at 16:36, Dan Zuras Intervals wrote:
Both are reasonable functions to demand we have lying
around for use by 1788.
But both are Real functions of Real or integer powers.
In 1788 we are in the business of defining interval
functions of interval arguments.
I am wondering if there is a misunderstanding going on. Of course,
very possibly I am the one who is misunderstanding...
It is fairly explicit in Motion 6 that an interval elementary
function ee is, by definition, an interval extension of a point
elementary function e. (Things like hull(xx,yy) and intersection
(xx,yy) are not of this kind, and are called interval mappings, not
functions.) So for each e, there are basically just two things for
P1788 to decide:
(1) a precise definition of e's domain, and value at each point of
the domain;
(2) how tight we require the interval extension to be, as measured
e.g. by Vienna's "tight", "accurate" or "valid".
If we decide "tight" then ee is unique: it has to be the "natural
interval extension".
I think Motion 7 states it is not about (2), which is to be decided
later (by a subgroup, I personally hope).
Hence Motion 7 is just about (1), that is,
about agreeing a list of precisely specified point
functions of real variables.
Note that, (as Vienna says) pown(a,p) or in Vienna's notation a
intpow p, is not regarded as one function of 2 variables (real,int),
but as a family of functions pown(. , p) of one real variable.
John