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Analytic geometry in two dimensions
1.1 Real numbers Without undertaking an exhaustive exposition of
the subject, this preliminary section presents fundamental ideas about
arithmetic, geometry, and algebra that are used throughout the book.
While much of the material will be familiar, students are expected to read
everything (including the problems) to assimilate information and points
of view required for comprehension of later sections of the book. The
rules of our game must be unmistakably clear at all times. We read
everything, and we work some of the problems.
The numbers with which we are most familiar are the positive real
numbers. These are the numbers, such as 1, 1, 2, 7r, 416, etcetera,
that represent weights of material objects, distances between towns,
etcetera. The negative real numbers are the negatives of these, examples
being --, -1, and - N/12. These positive and negative real numbers,
together with 0, which is neither positive nor negative, constitute the set
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