ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book is concerned with all aspects of the infinite, mathematical and non-mathematical alike as the author remarks about the centrality of the fourth kind of paradox ought to have suggested; for paradoxes of thought about the infinite are certainly not — exclusively — mathematical. Metaphysical concepts are to the fore in the book alongside mathematical concepts. These paradoxes fall into four groups: paradoxes of the infinitely small; paradoxes of the infinitely big; paradoxes of the one and the many; and paradoxes of thought about the infinite. The first two groups reflect an important distinction within the mathematically infinite between what Aristotle called the infinite by division and the infinite by addition: a straight line.
