Problem 6: Something That Isn't Small Monsters (20)

While the Small Monster collector, researcher, ecclesiastical historian and tournament spectator was busy with marmosets, we showed in class that we can an assign an integer order to the members of an infinite two-dimensional array; and thus, that infinite two-dimensional arrays are countable, and can be re-ordered as infinite one-dimensional arrays. Using that result, prove by induction that for any positive integer , an infinite -dimensional array is countable.