This appendix treats some topics that are likely to be well known by some readers and less known by others. Most of it already comes into play by Chapter II. Section A1 deals with set theory and with functions: it discusses the role of formal set theory, it works in a simplified framework that avoids too much formalism and the standard pitfalls, it establishes notation, and it mentions some formulas. Some emphasis is put on distinguishing the image and the range of a function, since this distinction is important in algebra and algebraic topology.
Section A2 defines equivalence relations and establishes the basic fact that they lead to a partitioning of the underlying set into equivalence classes.
Section A3 reviews the construction of rational numbers from the integers, and real numbers from the rational numbers. From there it concentrates on the solvability within the real numbers of certain polynomial equations.
Section A4 is a quick review of complex numbers, real and imaginary parts, complex conjugation, and absolute value.
Sections A5 and A6 return to set theory. Section A5 defines partial orderings and includes Zorn's Lemma, which is a powerful version of the Axiom of Choice, while Section A6 concerns cardinality.
Digital Object Identifier: 10.3792/euclid/9781429799980-11