Primitive Sequences and Sets of Multiples

Throughout this chapter A = {a _i } will denote a subsequence of the sequence of natural numbers. We consider the set ℬ = ℬ(A) consisting of all the distinct positive multiples of elements of A. We note that ℬ is the positive part of the union, taken over all elements a _i of A, of the congruence classes 0 (mod a _i ). Whilst none of our arguments will depend on ordering ℬ, it will often be convenient (to facilitate description and for reasons of notation) to imagine ℬ to be ordered according to magnitude and to refer to it as a ‘sequence’.