Abstract
The derivative is one of the fundamental concepts of calculus. The definition of derivative, at first glance, appears to involve division by zero, and division by zero is not permitted. The inventors of calculus, Newton and Leibniz, were aware of this difficulty and attempted to meet the criticisms of their contemporaries. However it took about 200 years for mathematicians to put the foundations of calculus on what is now considered a satsifactory basis. In this essay an explanation of the problem will be given followed by a description of some mathematical stumblings, culminating in the present-day solution. Discussion of how to teach this material to first-year students of calculus will conclude the essay. It is hoped that this presentation will be comprehensible to someone who has studied calculus for a semester.
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Dedicated to my father
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© 1974 D. Reidel Publishing Company, Dordrecht-Holland
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Struik, R.R. (1974). Some Remarks on the Concept of Limit. In: Cohen, R.S., Stachel, J.J., Wartofsky, M.W. (eds) For Dirk Struik. Boston Studies in the Philosophy of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2115-9_10
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DOI: https://doi.org/10.1007/978-94-010-2115-9_10
Publisher Name: Springer, Dordrecht
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