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What would be the decorated intermediate results for ( 1/(atan([\pi/4,\pi/2]) )^2 ? Baker On 02/18/2013 09:00 AM, John Pryce wrote:
Vincent On 18 Feb 2013, at 10:07, Vincent Lefevre wrote:On 2013-02-16 15:40:11 +0000, John Pryce wrote:The dac, together with the bounded input(s), suffices to prove that all the intermediate values, as well as the output, are mathematically bounded, by compactness. (A continuous function on a compact set is bounded.) I think this was my reason for saying that com should describe what actually happens at Level 2, rather than what ideally happens at Level 1. Namely, I claim that your i2+o2 can never produce more informative results than what such a compactness argument can produce using i1+o1. And that there is no other good reason to move to i2 and/or o2.I agree. This is what I said in our private discussion in November:...Thanks for circulating that. It's "obvious when you see it" but easy to forget why it's obvious. It needs spelling out in a Note to the main text somewhere. John
-- --------------------------------------------------------------- Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA ---------------------------------------------------------------