Steve W. wrote: << [I wrote] << Let x_n be a dense sequence in [0,1]. x_1 divides [0,1] into a left piece of length a_1 and a right piece b_1. Inductively, x_(n+1) divides one of the subintervals that {x_1,...,x_n} divide [0,1] into a left piece of length a_n and a right piece of length b_n.

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Shouldn't x_(n+1) divide into a_(n+1) and b_(n+1) ?

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Yes, that's what I should have written. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele