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RISS 인기검색어
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- 저자 : William C. Waterhouse (검색결과 1 건)
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William C. Waterhouse 江南大學校産學技術硏究所 1996 산학기술연구소논문집 Vol.- No.2
"The main foundational results of calculus can be derived directly from the statement that bounded increasing sequences converge." The foundations of calculus are well understood by specialists, but they are always hard to convey to students trying to learn them. One of the obstacles, I think, is that most treatments of the subject find it necessary to introduce various technical definitions (for instance, uniform continuity and least upper bounds). These concepts are of course important in themselves, but their complexity makes them hard for students who are just beginning to understand limits. In this presentation of the subject, I shall derive the main foundational results purely from one fact: A bound increasing sequence of real numbers converges. It is well known that this is the property behind the crucial comparison test for infinite series, but few people seem to know how easily it can be used more generally. In particular, the argument for Theorem 2 here seems to be new.
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