Re: Midpoint and unbounded intervals
On 2012-01-24 14:16:29 -0600, Nate Hayes wrote:
> Dear P1788,
>
> Dan Zuras and myself had an offline discussion about the midpoint and width
> operations over the past couple weeks. We decided to summarize our
> agreements and present them as a paper to the rest of the group for further
> discussion. With his permission, I am therefore attaching that paper to this
> e-mail.
>
> Comments are welcome.
The only real problem I've seen is the point mentioned by Dmitry
(and which will be fixed).
(11) will generally not hold at Level 2: one would just have the
implication =>, not the equivalence.
For midpoint(Entire), I think it should be undefined at Level 1,
and 0 is OK for inf-sup at Level 2.
A property that should be satisfied is:
X <= Y => midpoint(X) <= midpoint(Y)
for any non-empty X, Y. If I'm not mistaken, it is satisfied by (15).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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