Set Theory

An Introduction to Axiomatic Reasoning
1. Auflage 2025
ISBN: 978-1-032-95482-0
Verlag: Taylor & Francis Ltd

Buch, Englisch, 442 Seiten, Format (B × H): 162 mm x 242 mm, Gewicht: 800 g

Reihe: Textbooks in Mathematics

Contemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written decades ago, and now considered to be “classics”, are still prescribed for students today. These texts are not suitable for today’s students. This text is meant for and written to today’s mathematics students.

Set theory is a pure mathematics endeavor in the sense that it seems to have no immediate applications; yet the knowledge and skills developed in such a course can easily branch out to various fields of both pure mathematics and applied mathematics.

Rather than transforming the reader into a practicing mathematician, this book is more designed to initiate the reader to what may be called “mathematical thinking” while developing knowledge about foundations of modern mathematics. Without this insight, becoming a practicing mathematician is much more daunting.

The main objective is twofold. The students will develop some fundamental understanding of the foundations of mathematics and elements of set theory, in general. In the process, the student will develop skills in proving simple mathematical statements with “mathematical rigor”.

Carefully presented detailed proofs and rigorous chains of logical arguments will guide the students from the fundamental ZFC-axioms and definitions to show why a basic mathematical statement must hold true. The student will recognize the role played by each fundamental axiom in development of modern mathematics. The student will learn to distinguish between a correct mathematical proof and an erroneous one. The subject matter is presented while bypassing the complexities encountered when using formal logic.

Zielgruppe

Undergraduate Advanced

Autoren/Hrsg.

Andre, Robert

André, Robert

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mengenlehre

Inhaltsverzeichnis

1 Axioms and classes

2 Class operations

3 Relations

4 Functions

5 From sets to numbers

6 Infinite sets

7 Cardinal numbers

8 Ordinal numbers

9 More on axioms: Choice, regularity and Martin's axiom

10 Ordinal arithmetic

Über Autor(innen)

Robert André recently completed 18 years as a lecturer in the Department of Pure Mathematics, at the University of Waterloo, Ontario, Canada. He earned a PhD from the University of Manitoba specializing in point-set topology. He has taught high school mathematics for 14 years in Manitoba, Saskatchewan, and New Brunswick. Dr. André has lectured general and honors courses at all levels in the undergraduate program.