In this book I have endeavored to develop the theory of the algebraic processes in as elementary and informal a manner as possible, but connectedly and rigorously, and to present the processes themselves in the form best adapted to the purposes of practical reckoning.
The book is meant to contain everything relating to algebra that a student is likely to need during his school and college course, and the effort has been made to arrange this varied material in an order which will properly exhibit the logical interdependence of its related parts.
It has seemed to me best to divide the book into two parts, a preliminary part devoted to the number system of algebra and a principal part devoted to algebra itself.
I have based my discussion of number on the notion of cardinal number and the notion of order as exhibited in the first instance in the natural scale 1, 2, 3, .... There are considerations of a theoretical nature in favor of this procedure into which I need not enter here. But experience has convinced me that from a pedagogical point of view also this method is the best. The meaning of the ordinal definition of an irrational number, for example, can be made clear even to a young student, whereas any other real definition of such a number is too abstract to be always correctly understood by advanced students.
My discussion of number may be thought unnecessarily elaborate.