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!mhuxr!mhuxj!houxm!hou2g!vdb From: vdb@hou2g.UUCP (R.VANDERBEI) Newsgroups: net.math Subject: Re: Any number as infinite series Message-ID: <385@hou2g.UUCP> Date: Thu, 10-Jan-85 14:25:42 EST Article-I.D.: hou2g.385 Posted: Thu Jan 10 14:25:42 1985 Date-Received: Sat, 12-Jan-85 01:11:47 EST References: <17957@lanl.UUCP> <28200048@uiucdcs.UUCP>, <1088@aecom.UUCP> Organization: AT&T Bell Labs, Holmdel NJ Lines: 16 Lets get it straight! Real numbers are by definition limits of rationals: x = lim r(n). Hence any real number can be written as an infinite series of rational numbers: x = r(0) + [r(1)-r(0)] + [r(2)-r(1)] + ... An infinite series is by definition a limit of partial sums. In fact the notions are equivalent: every infinite series can be written as a limit and every limit can be written as an infinite series. .