Re: Motion P1788/M0012.01:InnerAdditionAndSubtraction
Alexandre (and P-1788, this is the culmination of a private discussion),
Ah, you are right. I made a couple of errors. With the new value
of y, we just compute the new value of z, rather than of x. I should have said:
.
.
.
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original statement. In particular, suppose we have x and y point values,
and we know
x + y = [-8,13],
where we originally knew x \in [2,3] and y \in [-10,10] and found
the bound [-8,13] by adding the intervals. Suppose now, by independent
means, we find y \in [1,2]. We would have
x \in [-8,13] - [1,2] = [-10,12],
no improvement in x, and
x \in [-8,13] \cancelminus [1,2] = [-9,11], (**)
also no improvement. However, is the conclusion x \in [-9,11]
even correct (for this use of \cancelminus in general)?
What definitely is correct is
*
*
\*/
*
z \in ([-8,13] \cancelminus [-10,10]) + [1,2]
= [2,3] + [1,2] = [3,5].
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My original statement,
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x \in ([-8,13] \cancelminus [-10,10]) + [1,2]
= [2,3] + [1,2] = [3,5].
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was certainly incorrect. Also, z would have to have been reduced through
some other method for (**) to result in an improvement, in which case, as
you have privately asserted, the \cancelminus would not be appropriate.
In any case, \cancelminus is convenient, aside from my blunders here.
Baker
On 3/22/2010 1:23 PM, Alexandre Goldsztejn wrote:
Dear Professor Kearfott,
I am sorry I don't follow neither!
You have an original domain [2,3] for x, and then you compute using
inner operation a new domain [3,5] for x. Shouldn't I intersect these
two domains to obtain [3,3] as a better domain for x?
Alexandre
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R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
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