First Properties of ℝ
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Chapter 1 lays the foundation; what are we building? Our most ambitious objective is to give a logically rigorous presentation of Calculus, learning as much as possible along the way. Everything has to come from the axioms for the field of real numbers ℝ (that in fact it does seems a miracle!). The properties of ℝ developed in this chapter lie very close to the axioms; they require some ingenuity but no essential new concepts (such as limits).
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