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Unformatted text preview: BAIN MUSC 525 PostTonal Music Theory BAIN Set Theory , 1 of 2 Set Theory “A set may be viewed as any welldefined 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 sets…Thus set theory is, in a sense, the foundation on which virtually all of mathematics is constructed.” B. Kolman and R. Busby, Discrete Mathematical Structures “Zermelo–Frankel set theory…is 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 axioms…The 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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 Spring '08
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 Math, Set Theory, Sets, Discrete Mathematical Structures, Bernard Kolman, BAIN MUSC

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