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Proof by induction consists in following scheme:

Proof by induction

or intuitively, let be a predicate $ P(n) $ with $ n \in \Bbb{N} $:

if

  1. $P(0) $ is true
  2. $P(k)\to P(k+1), \forall k \in \Bbb{N} $ is true

then $P(n), \forall n \in \Bbb{N}$ is true

but can I proof by contradiction the point 2?

mle
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1 Answers1

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You can prove however you want either point 1 or 2. As long as their proofs are valid, by the induction theorem you can conclude that $P$ holds for all natural numbers.

frabala
  • 3,732