Re: Friendly amendment to Motion 25
On 2011-05-28 12:25:11 -0500, Nate Hayes wrote:
> In light of recent discussions, I submit the attached PDF as a friendly
> amendment to Motion 25.
Here are my comments:
Definition 1 is an equivalence. But how about h(x) = Zero(u(x)),
where Zero is the constant unary function with the value 0 when
u is not continuous? i.e. what if one wants to allow user-defined
functions built from basic functions? I think that one may need
to have decorations saying that C(f,X) is unknown.
One would have: u(x) would give some decorated interval (X,DD_2).
T(Zero,(X,DD_2)) = inf(S(Zero,RR),DD_2) = inf(DD_3,DD_2) = DD_2,
even though h is continuous over X. One may accept that decorations
are pessimistic even when the enclosure (here, [0,0]) is optimal,
but the first paragraph of the rationale says "and in the case the
enclosure is optimal, the decoration is also exact".
Similar example when Level 2 is involved:
sqrt(1/x - 1/x) * 0 over X = [3,3].
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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