User blog comment:Wythagoras/Friendship function/@comment-1605058-20140717204945/@comment-10429372-20140718062220

Your argument doesn't work, beacause we can go from

(p,p,p)=w^(w^2*3) to

(o,q)(o,q)(o,q) = w^(w^3+w)*3

Also, if one friendship is minor of another, then associated ordinal is smaller, beacause both the number of brackets and the number of friends are smaller.