Fundamental Concepts

  • Anthony N. Michel
  • Charles J. Herget


In this chapter we present fundamental concepts required throughout the remainder of this book. We begin by considering sets in Section 1.1. In Section 1.2 we discuss functions; in Section 1.3 we introduce relations and equivalence relations; and in Section 1.4 we concern ourselves with operations on sets. In Section 1.5 we give a brief indication of the types of mathematical systems which we will consider in this book. The chapter concludes with a brief discussion of references.


Real Number Equivalence Relation Proper Subset Fundamental Concept Injective Mapping 


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  1. [1.1]
    A. M. Gleason, Fundamentals of Abstract Analysis. Reading, Mass.: Addison-Wesley Publishing Co., Inc., 1966.MATHGoogle Scholar
  2. [1.2]
    M. E. Goldstein and B. M. Rosenbaum, “Introduction to Abstract Analysis,” National Aeronautics and Space Administration, Report No. SP-203, Washington, D.C., 1969.Google Scholar
  3. [1.3]
    P. R. Halmos, Naive Set Theory. Princeton, N.J.: D. Van Nostrand Company, Inc., 1960.MATHGoogle Scholar
  4. [1.4]
    C. B. Hanneken, Introduction to Abstract Algebra. Belmont, Calif.: Dickenson Publishing Co., Inc., 1968.MATHGoogle Scholar
  5. [1.5]
    F. Hausdorff, Mengenlehre. New York: Dover Publications, Inc., 1944.MATHGoogle Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Anthony N. Michel
    • 1
  • Charles J. Herget
    • 2
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Herget AssociatesAlamedaUSA

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