leimkuhl@uiuccsb.UUCP (11/03/83)
#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