## Abstract Predecessor Tree is Composed of *Unique* Infinite Subsets of Odd Integers

### -- a) by construction: successive
subdivision of root node set

-- 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

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