Essential Concepts of Set Theory

Robert S. Y. Wong, Manwai Yeung

For thousands of years, it is generally believed that mathematics begins with the natural numbers and counting. But there is something more fundamental than counting. It is the grouping of things. If a child is shown a picture of a farm with sheep and cows here and there and asked to count the number of sheep, the child would first put the sheep in a group mentally and then count the number of sheep in the group. Without grouping, counting cannot happen. Therefore, mathematics begins with the grouping of objects, which is the object of study of set theory.

In this book, we explore the fundamental concepts of sets and related topics: propositional logic, methods of proof, relations and functions. Unlike the technical approach adopted in most books, we use many everyday examples to show that these concepts can be found everywhere in our daily life. The book also has plenty of exercises and solutions to all exercises are provided.


Robert S. Y. Wong, Manwai Yeung

Dr. Robert Sing Yen Wong obtained his PhD in Pure Mathematics from the University of New South Wales, Australia. He is currently a teacher of Olympiad mathematics in Hong Kong. Dr. Manwai Yuen obtained a PhD in Applied Mathematics from the Hong Kong Polytechnic University. He is currently an Assistant Professor in the Department of Mathematics and Information Technology, the Education University of Hong Kong.




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