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Unformatted text preview: x such that p ( x ) is true. Example: Prove that the following is not valid rstorder formula: x (  ) (( x ) ( )) . January 18 Proofs, Page 4 5.1 Proof methods Proof by induction: to prove For any integer n 0, P ( n ). Prove that P (0) is true. Prove that for any integer i 0, P ( i ) P ( i + 1). Conclude that P ( n ) is true for all n 0. Correctness: by axiom of natural numbers. Example: Prove that for any n 0, 0 + 1 + 2 + + n = n ( n + 1) / 2. Prove that 2 b n 2 for all n 4. January 18 Proofs, Page 5 5.2 Proofs that go wrong . Mistaken : To prove p : we know p q and q , therefore, p . To prove xP ( x ): here are examples of x that P ( x ) is true, thus P ( x ) must be true for all x . January 18 Proofs, Page 6...
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This note was uploaded on 04/01/2008 for the course EECS 203 taught by Professor Yaoyunshi during the Winter '07 term at University of Michigan.
 Winter '07
 YaoyunShi

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