Results 221 to 230 of about 82,468 (248)
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Second-order Non-nonstandard Analysis
Studia Logica, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2001
Classical or standard analysis is mostly concerned with the study of the real numbers and with the properties of functions defined on them. We shall now describe the use of the hyperreals as valuable tools for mathematical analysis. Through the existence of infinitesimals, finite, and infinite numbers, NSA provides us with a rich structure which we use
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Classical or standard analysis is mostly concerned with the study of the real numbers and with the properties of functions defined on them. We shall now describe the use of the hyperreals as valuable tools for mathematical analysis. Through the existence of infinitesimals, finite, and infinite numbers, NSA provides us with a rich structure which we use
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The American Mathematical Monthly, 1973
[no abstract] ; © 1973 Mathematical Association of America. Work on this paper was also supported in part by Grant No. GP-7691 from the National Science Foundation.
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[no abstract] ; © 1973 Mathematical Association of America. Work on this paper was also supported in part by Grant No. GP-7691 from the National Science Foundation.
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1997
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 ...
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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 ...
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Introduction to nonstandard analysis
Journal of Mathematical Physics, 1973Nonstandard analysis is a recent branch of mathematics in which usual notions about analysis and topology can be formulated in an attractive and condensed manner. The main feature of this theory is that it introduces the concept of infinitely large or small numbers and that it allows one to compute with them in exactly the same way as in ordinary ...
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1983
In diesem Kapitel wollen wir den Korper ℝ der reellen Zahlen zu einem Korper *ℝ erweitern, in dem es unendlich kleine und unendlich grose „Zahlen“ gibt. Insbesondere lassen sich in *ℝ die Leibnizschen Differentiale dx, dy exakt definieren und ein Zusammenhang des Differentialquotienten dy/dx mit der Ableitung f’(x) einer Funktion y = f(x) an der Stelle
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In diesem Kapitel wollen wir den Korper ℝ der reellen Zahlen zu einem Korper *ℝ erweitern, in dem es unendlich kleine und unendlich grose „Zahlen“ gibt. Insbesondere lassen sich in *ℝ die Leibnizschen Differentiale dx, dy exakt definieren und ein Zusammenhang des Differentialquotienten dy/dx mit der Ableitung f’(x) einer Funktion y = f(x) an der Stelle
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