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 July 14th, 2016, 05:54 AM #11 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,166 Thanks: 738 Math Focus: Physics, mathematical modelling, numerical and computational solutions Let my sandwich be a cheese sandwich After I put my glasses on, it turns out not to be a cheese sandwich. Therefore, contradiction! Gadzooks! The nature of cheesiness of sandwich hath revealed itself unto me! Thanks from topsquark and manus July 14th, 2016, 09:49 AM   #12
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 Let my sandwich be a cheese sandwich After I put my glasses on, it turns out not to be a cheese sandwich.
That is because it was a chose sandwich - y'all chose it.  July 14th, 2016, 11:58 AM   #13
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 Originally Posted by studiot That is because it was a chose sandwich - y'all chose it. Wouldn't that be using the axiom of sandwich choice? -Dan July 14th, 2016, 05:46 PM   #14
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 Originally Posted by zylo I stick by my original contention. If f(x) is continuous on a closed interval, it can never equal $\displaystyle \infty$.
You obviously didn't read my last post carefully enough, as you made exactly the same mistake in this statement as you did before. July 27th, 2016, 01:41 PM #15 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 I give up. Can't think of a simple, elementary, proof of OP. So: Since f continuous, for every p of [a,b] |f(x)-f(p)| < $\displaystyle \epsilon$ if |x-p| < $\displaystyle \delta_{p}$ Snce f continuous, f(p) finite, and f(p)- $\displaystyle \epsilon$ < f(x) < f(p) + $\displaystyle \epsilon$ < Mp For every point p there is an interval p-$\displaystyle \delta_{p}$< x < p+$\displaystyle \delta_{p}$ on which f(x) is bounded. These intervals cover [a,b]. By Heine-Borel theorem there is a finite subset of the intervals which cover [a,b]. Then f(x) is bounded by the max value of Mp on these intervals. Tags bounded, closed, continuous, function, interval Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post dpsmith Real Analysis 11 September 1st, 2015 05:53 PM king.oslo Real Analysis 1 July 7th, 2014 05:30 AM natt010 Real Analysis 3 May 4th, 2014 03:51 PM leeSono Real Analysis 2 October 4th, 2013 10:02 AM rose3 Real Analysis 1 December 19th, 2009 02:06 PM

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