Abstract Predecessor Tree is Composed of Unique Infinite Subsets of Odd Integers
-- a) by construction: successive
subdivision of root node set
return to slide index
-- all sets at any level are disjoint
-- all sets in l.d.a.s are disjoint
-- sets in separate branches of the tree are disjoint
-- leaf sets "on the way down during
formula development" are subsets of their parents but become disjoint "on the way back up"
-- b) by examination of characterizing formulas
-- Two subsets, defined by d*n+c
and d'*n+c' are disjoint iff c and c' are not congruent mod gcd(d,d').
-- proof is again due to Margaret Maxfield
-- see a different picture