This preview shows page 1. Sign up to view the full content.
Unformatted text preview: FIRST YEAR CALCULUS
W W L CHEN
W W L Chen, 1982, 2005. This chapter originates from material used by the author at Imperial College, University of London, between 1981 and 1990. It is available free to all individuals, on the understanding that it is not to be used for ﬁnancial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners. Chapter 1
THE NUMBER SYSTEM 1.1. The Real Numbers The purpose of the ﬁrst four sections of this chapter is to discuss a number of the properties of the real numbers. Most readers will be familiar with these properties, or have at least used most of them, perhaps sometimes unaware of their generality. We do not propose to discuss here these properties in great detail, and shall only give a brief introduction. Throughout, we denote the set of all real numbers by R, and write a ∈ R to indicate that a is a real n...
View Full Document