Titlebook: Mathematics of Discrete Structures for Computer Science; Gordon J. Pace Textbook 2012 Springer-Verlag Berlin Heidelberg 2012 discrete math

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Defining New Structured Types,This chapter shows how new structured types can be defined and reasoned about. The axiomatisation of such new types is presented, including the notion of structural induction—a concept central in computer science. The chapter uses various examples from computing, including lists, trees and data processing.

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Predicate Calculus, which a predicate holds requires a formalism richer than propositional logic. This chapter introduces the notion of predicates and extends the axiomatic approach presented in the previous chapter for propositional logic to allow formal reasoning about them.

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Sets, and standard set operators such as union, intersection, set complement and set difference are formally defined. Various properties about sets and the set operators are also proved using predicate logic. The chapter closes with a discussion of the importance of types in set theory.

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https://doi.org/10.1007/978-3-642-29840-0discrete mathematics; discrete structures; mathematical logic; predicate calculus; propositional logic; r

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Gordon J. Paceng lasting adjustment periods and locally or globally unstable equilibria. Variables such as real wages and employment may undergo persistent cycles of finite and infinite order. Although these models are highly stylized, and would not perform satisfactorily when confronted with real data, they can