## How to read and do proofs: an introduction to mathematical thought processesThis book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied. |

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### Contents

The Truth of It All | 2 |

The ForwardBackward Method | 9 |

On Definitions and Mathematical Terminology | 23 |

Copyright | |

10 other sections not shown

### Common terms and phrases

Analysis of Proof angle apply specialization assume assumption that P(n backward process choose method chosen object completing the proof construction method contains the quantifier contradiction method contrapositive method convex function convex set defining property desired conclusion divides element equal equivalent example exercises marked false following condensed proof following statements for-all statement foregoing forward process function happens http://www.wiley.com/college/solow hypotenuse integer namely Interpretation of S2 least upper bound max/min methods nested quantifiers number x obtain odd integer particular object positive integer prime proof is complete Proof of Proposition proof techniques proofs should contain Proposition 13 Pythagorean theorem reach a contradiction reach the conclusion Recognizing the key rewrite right triangle satisfies set of real set-builder notation show that Bl shown Solutions to exercises statement A implies statement containing statement is true steps subset Suppose symbol triangle RST truth table variable verify World Wide Web XYZ is isosceles