Suppose you have a rectangular lattice which extends infinitely both left to right and top to bottom and let the upper left hand corner be called the orgin. Problem for thought. Provide a first infinite sequence across the top of the lattice such that the nth lattice point to the right of the orgin contains the nth term of the sequence and define basic some operation that uniformly and completely defines the numbers assigned to the lower rows of the lattice based upon the terms above it so that the entire lattice points are predefined. How many of these lattices can you construct such that each of the integers from 1 to infinity will populate the lattice once and only once? There are in fact an infinite number such distinct lattices. Anyone care for an example or to give an example?