# A Primer of Real Functions

RALPH P. BOAS
revised and updated by HAROLD P. BOAS
Volume: 13
Edition: 4
Pages: 321
https://www.jstor.org/stable/10.4169/j.ctt5hh8x5

1. Front Matter
(pp. i-vi)
2. Preface to the Fourth Edition
(pp. vii-viii)
Harold P. Boas
3. Preface to the Third Edition
(pp. ix-xii)
Ralph P. Boas Jr.
(pp. xiii-xiv)
5. Chapter 1 Sets
(pp. 1-76)

In order to read anything about our subject, you will have to learn the language that is used in it. I have tried to keep the number of technical terms as small as possible, but there is a certain minimum vocabulary that is essential. Much of it consists of ordinary words used in special senses; this practice has both advantages and disadvantages, but has in any case to be endured since it is now too late to change the language completely. Much of the standard language is taken from the theory of sets, a subject with which we are not...

6. Chapter 2 Functions
(pp. 77-194)

In elementary mathematics, it is customary to say thatyis a function ofxif, whenxis given,yis determined (uniquely; we are not concerned with “multiple-valued functions”). This is a good working definition and one that suffices for most practical purposes. However, we should realize that it does not define function,” although it does give a definite meaning to some phrases containing this word. (In a somewhat similar way, we are accustomed to attaching a definite meaning to the phrase “y→ ∞” even though ∞ by itself has no meaning.) However, it is interesting, and...

7. Chapter 3 Integration
(pp. 195-244)

So far, we have mostly been dealing, directly or indirectly, with what used to be called differential calculus, and was clearly separated from integral calculus. The word “integral” has generally been used in two different senses. One is the process of undoing differentiation to find what have been variously described as antiderivatives, primitives, or indefinite integrals. This is the technique of finding explicit formulas for antiderivatives, an art which has lost much of its importance now that there are not only extensive tables of antiderivatives, but also computer programs that can find antiderivatives faster than people can find them by...