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From: leimkuhl@uiuccsb.UUCP
Newsgroups: net.math
Subject: Re: A question on enumerating the ration - (nf)
Message-ID: <3627@uiucdcs.UUCP>
Date: Wed, 2-Nov-83 20:32:26 EST
Article-I.D.: uiucdcs.3627
Posted: Wed Nov  2 20:32:26 1983
Date-Received: Sun, 6-Nov-83 09:35:48 EST
Lines: 17

#R:unc:-602900:uiuccsb:9700012:000:544
uiuccsb!leimkuhl    Nov  2 19:25:00 1983



>From a friend at Purdue I get the following simple solution to the first
problem:
	Let {an} be an enumeration of the rationals, and let {qn} be such
	that q1=a1, q2=-a1, q3=a2, q4=-a2,..,q(2n-1)=an, q(2n)=-an,... then
	the partial sums r1=q1, r2=q1+q2,... are just the sequence
	(a1,0,a2,0,a3,0,...) which clearly spans the rationals.

In this example, neither {qn} nor {rn} is without repitition, and the example
here sheds no light on the (probably much more difficult) problem of finding
{qn} and {rn} either or both WOR.

-Ben Leimkuhler