Abstract
Throughout this book, we frequently considered our familiar sets of numbers: \(\mathbb {N}\): the set of natural numbers; \(\mathbb {Z} \): the set of integers; \( \mathbb {Q}\): the set of rational numbers; \( \mathbb {R}\): the set of real numbers; and \( \mathbb {C}\): the set of complex numbers. We have already seen many of their distinguishing attributes, including some elaborate and far-reaching properties. But we have never, actually, defined these number sets; up till now, we treated them as primitives (cf. page 3). In this chapter we discuss how one can “build up” these number sets in the order above; we will also explain why, in a certain sense, \( \mathbb {C}\) cannot be—and needn’t be—enlarged further.
Published Version
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