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Unformatted text preview: BAIN MUSC 525 Post-Tonal Music Theory BAIN Set Theory , 1 of 2 Set Theory A set may be viewed as any well-defined collection of objects; the objects are called the elements or members of the set. The concept of a set appears in all branches of mathematics. This concept formalizes the idea of grouping objects together and viewing them as a single entity. Seymour Lipschutz, Set Theory and Related Topics Almost all mathematical objects are first of all setsThus set theory is, in a sense, the foundation on which virtually all of mathematics is constructed. B. Kolman and R. Busby, Discrete Mathematical Structures ZermeloFrankel set theoryis a rigorous theory, based on a precise set of axioms. However, it is possible to develop the theory of set considerably without any knowledge of those axiomsThe concept of a set of objects is a very intuitive one, and, with care, considerable, sound progress may be made on the basis of this intuition alone. Keith Devlin, The Joy of Sets Terms and Concepts Sets set theory - Naive - Axiomatic set ( see back for an intuitive definition...
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