Can you use $k-1$ in mathematical induction induction hypothesis
Rather than proving for the $k+1$ term?
Can you use k-1 in mathematical induction induction hypothesis
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discrete-mathematics
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0One way or another you need to prove $P(1)$ and $(\forall n \in \mathbb{N}) \: P(n) \Rightarrow P(n+1)$. The way you *write* that is up to you; for example, it is the same to prove $(\forall n \in \{ 2,3,\dots\}) \: P(n-1) \Rightarrow P(n)$, which would mean that your "inductive hypothesis" is $P(n-1)$ from which you need to infer $P(n)$. – 2017-02-10
1 Answers
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Yes.
Step 1 in the mathematical induction is to get a base case true. Step 2 is to prove that the claim holds for any $k \in \mathbb{Z}^+ $ with the hypothesis that the claim is true for $k-1$.
Note the "any" in step 2, that must answer your question.