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Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Discussions focus on rational numbers and ordered fields, ordering, arithmetic, axiom systems and methods of proof, functions of kindred matters, ordered pairs and relations, sets, and statements and open sentences. The text then examines real and complex numbers, metric spaces, and limits. Topics include generalized limits, continuous functions, openness, closedness, and neighborhood systems, definition and basic properties, and construction of R. The publication is a vital reference for mathematicians and students interested in abstract mathematics.
I. Logic and Set Theory
1.2 Statements and Open Sentences
1.4 Ordered Pairs and Relations
1.5 Functions and Kindred Matters
1.6 Axiom Systems and Methods of Proof
II. The Natural Numbers
III. The Integers and the Rational Numbers
3.3 Additional Topics
3.4 The Rational Numbers and Ordered Fields
IV. The Real and Complex Numbers
4.2 Construction of R
V. Metric Spaces
5.2 Definition and Basic Properties
5.3 Openness, Closedness, and Neighborhood Systems
5.4 Continuous Functions
6.2 Generalized Limits
6.3 Some Examples
Answers to Selected Exercises
- No. of pages:
- © Academic Press 1971
- 1st January 1971
- Academic Press
- eBook ISBN:
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