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. |
