Abstract
In this article we show how a nonstandard extension *ℝ of ℝ. can be used to formulate the fundamental ideas of infinitesimal calculus in a natural and intuitive way, and thereby develop real analysis rigorously based on these ideas. We include a number of exercises (which include proofs of results that are only slight developments of the theory) and encourage the reader who is new to this subject to work through as many of these as possible — for it is only by doing it that one can become fluent in the ideas and techniques of nonstandard analysis.
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© 1997 Springer Science+Business Media Dordrecht
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Cutland, N.J. (1997). Nonstandard Real Analysis. In: Arkeryd, L.O., Cutland, N.J., Henson, C.W. (eds) Nonstandard Analysis. NATO ASI Series, vol 493. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5544-1_2
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DOI: https://doi.org/10.1007/978-94-011-5544-1_2
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