Random Fortune

Theorem: All positive integers are equal.
Proof: Sufficient to show that for any two positive integers, A and B, A = B.
	Further, it is sufficient to show that for all N > 0, if A and B
	(positive integers) satisfy (MAX(A, B) = N) then A = B.

Proceed by induction:
	If N = 1, then A and B, being positive integers, must both be 1.
	So A = B.

Assume that the theorem is true for some value k.  Take A and B with
	MAX(A, B) = k+1.  Then  MAX((A-1), (B-1)) = k.  And hence
	(A-1) = (B-1).  Consequently, A = B.