Handbook of Mathematical Induction
Theory and Applications
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This comprehensive handbook enables readers to prove hundreds of mathematical results. It presents the formal development of natural numbers from axioms, which leads into set theory and transfinite induction. The book covers Peanoa (TM)s axioms, weak and strong induction, double induction, infinite descent downward induction, and variants of these inductions. It also contains numerous exercises highlighting the various levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. The final section includes solutions to all exercises in long form so that no steps are omitted.
This comprehensive handbook presents hundreds of classical theorems and proofs that span many areas, including basic equalities and inequalities, combinatorics, linear algebra, calculus, trigonometry, geometry, set theory, game theory, recursion, and algorithms. It derives many forms of mathematical induction, such as infinite descent and the axiom of choice, from basic principles. Requiring only a modest amount of mathematical maturity to understand most results and proofs, the book contains more than 750 exercises-with complete solutions to at least 500. It also includes nearly 600 bibliographic references, numerous cross references, and an extensive index of over 3,000 entries.
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