The real number system
In an elementary calculus course the student learns the techniques of differentiation and integration and the skills needed for solving a variety of problems which use the processes of calculus. Most often, the principal theorems upon which calculus is based are stated without proof, while some of the auxiliary theorems are established in detail. To compensate for the missing proofs, most texts present arguments which show that the basic theorems are plausible. Frequently, a remark is added to the effect that rigorous proofs of these theorems can be found in advanced texts in analysis.
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