[10] Let E be as above. Define the mapping · : N ×N →N by x, y = E(x)E(y).

(a) Show that · is a total one-to-one mapping and a prefix-code.

(b) Show that we can extend this scheme to k-tuples (n1, n2,...,nk) of natural numbers to obtain a total one-to-one mapping from N ×N ×

···×N into N that is a prefix-code.

Comments. Define the mapping for (x, y, z) as x,y, z and iterate this construction. Another way is to map (x, y, . . . , z) to E(x)E(y)...E(z).