Stories About Sets by N. Ya. Vilenkin (PDF)

Description

Stories About Sets discusses the cardinality of sets and mathematical concepts, such as function, curve, surface, dimensions, and the paradoxical properties of curves and surfaces. The book reviews sets, operations on sets, the empty set, subsets, the universal sets, intersection of sets, union of sets, partitioning of sets, and boolean algebras. The text also discusses the cardinality of sets, including equality between sets, countable sets, unequal sets, the uncountability of the continuum, the existence of transcendental numbers, and the enigmatic axiom. The book analyzes if a part can be equal to the whole (which turns out to be true if it is applied to infinite sets). The text also discusses the arithmetic of the infinite such as involving the multiplication of infinite cardinalities. The book explains some remarkable functions and curves, the Dirichlet’s function, Cantor’s set, points of fracture, and continuous functions whose graphs possess a tangent at no point. The text shows how to construct a closed curve of infinite length or a curve passing through all the points of a square. The book can prove interesting and highly educational for students with mathematic or algebra subjects, as well as for academicians involved in teaching statistics or mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Best quick intro to non-axiomatic Set Theory is probably that by Halmos, Naive Set Theory.Stories About Sets is up there with Halmos. Very readable with lots of examples.Recommended.

⭐After I read the first chapter of this book, I wish I had read it when I was an undergraduate. Basically, it teaches some basic topics of set theory and topology in a fun way. I think every math undergraduate should read it to get an intuitive idea about some of the main problems of these two areas in their beginning.The book starts with a story that is some kind of space-age version of Cantor’s infinite hotel. From Chapter 3 on, the book gives very intuitive and clear explanations of the concepts studied. Of course, the exposition is aimed at a mathematically minded individual. The topics covered in the book go from the concept of set and cardinality to the definition of curve (as a continuum of dimension 1). The reader will not only learn the mathematical ideas that gave origin to the concept of curve but also the historic setting. The ideas are all presented with their actual historic motivation.Perhaps the only part in which the book fails is the part of Chapter 2 in which the algebra of sets is introduced. I found it really tedious. However, it may be difficult to write about algebra of sets in an entertaining way. So if you get to this point and get bored, do not despair and wait till Chapter 3 when things will get entertaining again.

⭐Very gentle introduction to sets theory in facinate way.The books introduce to reader the heart of set theory by using wonderfull and interesting examples. The book suitable from age 10 +-.But will be interesting also for students and adults.I always use the example from this book when I teach my students discrete math in university.Thery good starting book

⭐This book, along with my geometry teacher Mr. Zell in the freshman year of high school, is partly responsible for the fact that I am a professional mathematician. Its opening chapter on the hotel with infinitely many rooms furnishes a memorable introduction to the idea of infinite sets.It is probably beyond the typical high school student; I am going to think about excerpting it for a college sophomore class.

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