The Statement: If a set of n balls contains a green ball then all the balls in the set are green.
The proof:
The statement holds trivially for n = 1. Assume that the statement is true for n ≤ k. Take a
collection $B_1$ of k + 1 balls that contains at least one green ball. From $B_{k+1}$, pick a collection $B_k$ of k balls that contains at least one green ball. Then by the induction hypothesis, each ball in $B_k$ is green. Now, remove one ball from $B_k$ and put the ball which was left out in the beginning. Call it $B_k'$. Again by the induction hypothesis, each ball in $B_k'$ is green. Thus, each ball in Bk+1 is green. Hence by PMI, our proof is complete.
What's the error?
