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Maths › 00. General Mathematics ›

01.2 Sets, Types, and Universes

1.2 Sets, Types, and Universes Mathematics needs a way to say what kind of thing an object is. Before we can prove a statement, define a function, or compare two objects, we need a domain of discourse. Sets, types, and universes provide different ways to organize that domain. A set is a collection of objects, called elements. We write: x ∈ A to mean that x is an element of...

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03. Logic and Foundations

This volume develops formal logic, set theory, computability, and the foundations of mathematics in a unified way, where syntax, semantics, proof, and computation are treated as precise mathematical objects. Part I. Propositional and First-Order Logic Chapter 1. Propositional Logic This chapter introduces the basic language of propositional logic, its semantics, equivalence laws, normal forms, and the relation between proof and truth. 1.1 Syntax: Variables, Connectives 1.2 Semantics: Truth Tables 1.3...