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I am writing a proof by mathematical induction.

I prove the base case: $n = 0$. In the inductive step I want to prove $P(n + 1)$ by assuming $P(n)$. As it turns out, to show $P(n+1)$ I need to rely on all $P(k), 0 \leq k \leq n$.

Is this possible? Or do I need to reconsider my proof strategy?

Hanul Jeon
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David Poxon
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  • yes,that's right.and notice that it's possible to have a base case which is not zero,actually the base case in the minimal element of the set which is going to be inducted, also you are using strong induction ,there exist another version named "weak induction" or "induction", indeed they are equivallent. – Absurd Dec 13 '19 at 07:41
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    That is called “complete/strong induction,” see for example https://en.wikipedia.org/wiki/Mathematical_induction#Complete_(strong)_induction – Martin R Dec 13 '19 at 07:41
  • Thanks, I didn't know strong induction was a thing. :) – David Poxon Dec 13 '19 at 07:59

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