From: SourceForge.net <no...@so...> - 2009-11-09 21:11:18
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Bugs item #2888450, was opened at 2009-10-29 02:21 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2888450&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Pending Resolution: Works For Me Priority: 5 Private: No Submitted By: Rudolf Vyborny (ynrobyvr) Assigned to: Nobody/Anonymous (nobody) Summary: wrong result Initial Comment: wrong result in calculating limit of x*floor(1/x) as x goes to 0 ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2009-11-09 22:11 Message: Sorry, I have no mathematical proof. I have come to the conclusion because of the follwing: 1. The function floor(x) is discontinuous. 2. The function x*floor(1/x) has an infinite number of points of discontinuity in any infinitesimal intervall when aproching zero. 3. Therefore, the function does not approach a limit. I could be wrong. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2009-11-09 18:17 Message: Isn't the limit 1? Let any x small enough, 1/x = n + e, where n is an integer and e < 1. Then floor(1/x) = n and x*floor(1/x) is n/(n+e) = 1 - e/(n+e). As n gets larger (and x gets smaller), this approaches 1. Did I make a mistake? ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2009-11-09 17:59 Message: With Maxima 5.19post I get a noun form too. There have been serveal changes the last time to improve limit. Furthermore, I think the limit of the example is not defined. Therefore, it seems to be not wrong to return a noun form. Setting the status to pending and works for me. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Rudolf Vyborny (ynrobyvr) Date: 2009-10-29 04:02 Message: I got the wrong result, namely 0. I attached my file ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2009-10-29 03:12 Message: I get the noun form back. Not wrong, but could be better. What were you expecting? ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2888450&group_id=4933 |