I don't understand the following assertion from "An Introduction to Recursive Partitioning" page 13.
If T1 and T2 are sub trees of T with Rα(T1) = Rα(T2), then either T1 is a sub tree of T2 or T2 is a sub tree of T1; hence either |T1| < |T2| or |T2| < |T1|.
I can easily built a symmetric tree (as far as the risk of a node is concerned) and the assertion will be false. I must be wrong but where is my miscomprehension.
I have read the source "L. Breiman, J.H. Friedman, R.A. Olshen, , and C.J Stone. Classification and Regression Trees. Wadsworth, Belmont, Ca, 1983." but it is not clear.
