Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site watmath.UUCP Path: utzoo!watmath!csc From: csc@watmath.UUCP (Computer Sci Club) Newsgroups: net.puzzle Subject: Re: Balls in Bowl (no correct answers yet) Message-ID: <6956@watmath.UUCP> Date: Mon, 20-Feb-84 15:03:30 EST Article-I.D.: watmath.6956 Posted: Mon Feb 20 15:03:30 1984 Date-Received: Tue, 21-Feb-84 07:47:26 EST References: <210@pucc-i> Organization: U of Waterloo, Ontario Lines: 23 The problem is similar to finding the sum of the series 100 - 1 + 100 - 1 + 100 - 1 ... As written the sum of the above series is infinity (ie the limit of the sequence of partial sums is infinity). However the subseries consisting of all negative terms is divergent. Hence we cannot rearange more than a finite number of terms and expect to have a limit for the sequence of partial sums. This is what is involved in such arguments as "number the balls sequentialy and say that machine B removes ball N at time noon - 1/N". If we assume the problem is find the sum of 100 - 1 + 100 -1 ..... and use the standard definition of the sum of a series, then the problem has a well defined answer, there will be an infinite number of balls in the bowl at noon. Else the argument "machine B removes ball N + K at time noon - 1/N" allows an arbitrary answer. (note also that infinity = limit as e goes to zero of the number of balls in the bowl at time noon - e) William Hughes