منابع مشابه
A New Approach to Nonstandard Analysis
In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing a few applications of this approach with the former methods.
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The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia's reasoning is resolutely geometric in nature but contains \in nitesimal" elements and the presence of motion that take it beyond the traditional boundaries of Euclidean Geometry. These present di culties that prevent Newton's proofs from being mechanised...
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1993
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496162143