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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<a,b<=n. From the inductive hypothesis, we know 2a=0, and 2b =0, therefore , 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.
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