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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.

.