> The diagonal sequence d_1, d_2, d_3, ..., is nested with d_n always a > subset of d_(n+1), so the natural limit is the same as the union. > > The sequence of bottom lines b_1, b_2, b_3, ..., are pairwise disjoint > sets so its union is not like another line but a concatenation of > disjoint lines, and has no equally natural limit.
Every b_n is as nested with its predecessors and is as numerous as the corresponding d_n. There is not the least reason (I mean resonable reason) why things should diverge "in the infinite".
