How to Read and Do Proofs: An Introduction to Mathematical Thought ProcessesWiley, 29 de març 1990 - 264 pàgines This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples. The Second Edition features new chapters on nested quantifiers and proof by cases, and the number of exercises has been doubled with answers to odd-numbered exercises provided. This text will be useful as a supplement in mathematics and logic courses. Prerequisite is high-school algebra. |
Continguts
The Truth of It All | 1 |
LIST OF TABLES | 4 |
The Truth of A implies B | 6 |
Copyright | |
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How to Read and Do Proofs: An Introduction to Mathematical Thought Process Daniel Solow Visualització de fragments - 1982 |
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Analysis of proof angle assume that P(n B1 is true backward process choose A1 choose method completing the proof condensed proof construction method contains the quantifier contradiction method contrapositive method convex function convex set cos(t defining property definition in Exercise divides element equal equation equivalent fact false following statements for-all statement forward process forward-backward method gives ƒ and g happens Hence hypotenuse induction integer namely key words mathematical method gives rise nested quantifiers number x obtain odd integer particular object prime problem Proof of Example proof techniques proposition Pythagorean theorem rational number reach a contradiction reach the conclusion real numbers rewrite right triangle set-builder notation show that B1 shown sides sin(t SOLUTIONS TO CHAPTER specialization specific statement A implies statement containing statement is true step subset Suppose symbol triangle RST Truth table uniqueness method upper bound verify XYZ is isosceles