Set-Theoretic Structures

Carlos S. Kubrusly ()
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 1 in The Elements of Operator Theory, 2011, pp 1-36 from Springer

Abstract: Abstract The purpose of this chapter is to present a brief review of some basic settheoretic concepts that will be needed in the sequel. By basic concepts we mean standard notation and terminology, and a few essential results that will be required in later chapters.We assume the reader is familiar with the notion of set and elements (or members, or points) of a set, as well as with the basic set operations. It is convenient to reserve certain symbols for certain sets, especially for the basic number systems. The set of all nonnegative integers will be denoted by $$\mathbb{N}_0$$ , the set of all positive integers (i.e., the set of all natural numbers) by $$\mathbb{N}$$ , and the set of all integers by $$\mathbb{Z}$$ . The set of all rational numbers will be denoted by $$\mathbb{Q}$$ , the set of all real numbers (or the real line) by $$\mathbb{R}$$ , and the set of all complex numbers by $$\mathbb{C}$$ .

Keywords: Equivalence Relation; Proper Subset; Complete Lattice; Injective Function; Cardinal Number (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-8176-4998-2_1

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