Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83 based; site hou2g.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!houxm!hou2g!stekas From: stekas@hou2g.UUCP (J.STEKAS) Newsgroups: net.puzzle Subject: Re: Balls in the bowl: Final word. Message-ID: <181@hou2g.UUCP> Date: Tue, 28-Feb-84 09:50:08 EST Article-I.D.: hou2g.181 Posted: Tue Feb 28 09:50:08 1984 Date-Received: Wed, 29-Feb-84 09:42:32 EST References: <220@pucc-i> <178@hou2g.UUCP>, <224@pucc-i> Organization: AT&T Bell Labs, Holmdel NJ Lines: 26 > Your arguments show quite convincingly that the limit of the number of balls > in the bowl, as time-->noon, is infinity. > > What makes you think the ACTUAL number of balls in the bowl at noon has > anything to do with the limit? ... Well, because the limit is the only meaningfull way of getting a unique answer. Dave's technique of numbering terms in the series can be used to generate any final result you want because it is an invalid operation. Example... Starting with an empty bowl, suppose at every t=12:00-1/n the number of balls in the bowl did not change. Taking the limiting case, at 12:00 the bowl would be in the same condition as when we started - empty. Taking Dave's approach, the number of balls can be made to "not change" by adding and removing a ball at each t=12:00-1/n giving a total number at noon = Sum( 1 + -1). Now cancell the -1 in every term against the +1 in the following term to get Sum(1 + -1)=1. Conclusion - if the number of balls is not changed at every t=12:00-1/n there will be 1 ball in the bowl. I'll leave it to the readers to decide which approach is correct. Jim