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"Sets and functions" as a book category covers the foundational language and tools of modern mathematics: basic set theory (elements, subsets, unions, intersections, power sets), relations and equivalence relations, and the theory of functions or mappings (domain, codomain, image, preimage, injective/surjective/bijective, composition and inverse). Books in this category typically develop precise notation and proof techniques, explore cardinality and countability of finite and infinite sets, and explain how functions encode structure-preserving maps used across algebra, analysis, topology, logic and computer science. They range from introductory texts for undergraduates and self-learners to more rigorous treatments that motivate axiomatic set theory and its role as a foundation for mathematics, often emphasizing examples, exercises, and applications that build abstract reasoning skills.

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