Abstract
It was hardly to be expected that the Axiom of Infinity would propel us inexorably from a discrete universe into a continuous one. But that is precisely what it does. And whether or not continuity is an intrinsic feature of creation, scientific enquiry into the mysteries of our world is greatly aided by a mathematics of continuity. This mathematics begins with a marriage of algebraic structure and order structure, from which arises a completely ordered field — essentially unique — which we call the Real Number System.
The several chairs of order look you scour With juice of balm and every precious flower: Each fair instalment, coat, and several crest, With loyal blazon, evermore be blest! And nightly, meadow-fairies, look you sing, Like to the Garter’s compass, in a ring. Merry Wives of Windsor, V,v.
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© 2002 Springer-Verlag London
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Searcóid, M.Ó. (2002). Analytic Structure. In: Elements of Abstract Analysis. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0179-6_4
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DOI: https://doi.org/10.1007/978-1-4471-0179-6_4
Publisher Name: Springer, London
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