Consider the following (false) claim and 'proof;' find the incorrect step. Claim: All positive integers are equal. Proof: 1. It suffices to show that for any two positive integers, A and B, A = B. 2. Further, it suffices to show that for all N > 0, if A and B are positive integers which satisfy MAX(A, B) = N, then A = B. 3. (Base Case) If N = 1, then A and B, being positive integers, must both be 1. So A = B. 4. (Induction Step) Assume that the theorem is true for some value k. Take positive integers A and B with MAX(A, B) = k+1. Then, MAX((A-1), (B-1)) = k. 5. Therefore, by induction, (A-1) = (B-1). Consequently, A = B. Hence, A = B for all positive integers A and B by induction. Q.E.D.

MCQs on Real Analysis.