The Logic of Infinity

by Barnaby Sheppard

Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

Genres: Logic, Philosophy, Mathematics

498 pages, Paperback

First published April 28, 2014

Reviews

[Michal Paszkiewicz · Rating 5 out of 5]

An excellent textbook, taking the reader through set theory and teaching them everything they need to know to understand the basics of infinity as it is treated within mathematics.

New ideas are introduced in baby steps and proofs are well presented so the reader doesn't need an advanced background in mathematics (although a bit of a background helps).