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Mathematical induction & Recursion

1M. HauskrechtCS 441 Discrete mathematics for CSCS 441 Discrete mathematics for CSLecture 15 Milos Sennott SquareMathematical induction & RecursionM. HauskrechtCS 441 Discrete mathematics for CSProofsBasic proof methods: Direct, Indirect, Contradiction, By Cases, EquivalencesProof of quantified statements: There exists x with some property P(x). It is sufficient to find one element for which the property holds. For all x some property P(x) holds. Proofs of For all x some property P(x) holds must cover all x and can be harder. Mathematical inductionis a technique that can be applied to prove the universal statements for sets of positive integers or their associated sequences.

2 CS 441 Discrete mathematics for CS M. Hauskrecht Mathematical induction • Used to prove statements of the form x P(x) where x Z+ Mathematical induction proofs consists of two steps: 1) Basis: The proposition P(1) is true. 2) Inductive Step: …

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