## The Nuts and Bolts of Proofs: An Introduction to Mathematical ProofsThe Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * The "List of Symbols" has been extended. * Set Theory section has been strengthened with more examples and exercises. * Addition of "A Collection of Proofs" |

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### Contents

1 | |

5 | |

9 | |

Chapter 4 Special Kinds of Theorems | 35 |

Chapter 5 Review Exercises | 103 |

Chapter 6 Exercises Without Solutions | 107 |

### Common terms and phrases

A O B Alleged Proof arbitrary number associative property composite statement consider construct a proof contrapositive convex sets counterexample counting numbers digits divides element equal to zero equation Example Exercise factor following statements formula front material function defined function f given statement graph greatest common divisor holds true Implicit hypothesis implies statement increasing function inductive hypothesis inequality inverse inverse function irrational number Let f Let us assume Let x e mathematical induction multiple natural numbers need to prove negative number is divisible number n obtain odd functions odd number one-to-one function original statement polynomial P(x positive integer number positive number possible prime number principle of mathematical Prove that lim rational number reciprocal relatively prime sequence smallest number solution statement is false statement is true statements are equivalent subsets theorem truth table unique values of f(x Venn diagrams want to prove write x1 and x2