Claim : For all non-negative integers, n ,2n =0 .

Proof : We will prove by strong induction on n. ;Base case : 2* 0 =0 . It is true for n =0. ;Inductive Hypothesis: Assume that 2k =0 for all 0<=k<=n.

Inductive step: we must show that 2(n+1) =0. Write n+1= a+b where 0

2(n+1) = 2(a+b) = 2a+2b = 0 +0 . so the statement is true.

The above claim is false. The proof is invalid. Please point out what is wrong with the proof.

Remark: simply saying that the claim or the induction hypothesis is false is not a valid explanations of what is wrong with the proof.