Get Conflicts between generalization, rigor, and intuition: PDF

By Gert Schubring

ISBN-10: 0387228365

ISBN-13: 9780387228365

This quantity is, as could be conveniently obvious, the fruit of a long time’ exertions in documents and libraries, unearthing infrequent books, learning Nachlässe, and specifically, systematic comparative research of fecund assets. The paintings not just demanded a lot time in training, yet used to be additionally interrupted by way of different tasks, resembling time spent as a visitor professor at universities in a foreign country, which after all supplied welcome possibilities to give and talk about the paintings, and specifically, the organizing of the 1994 foreign Graßmann convention and the following modifying of its complaints. whether it is impossible to be distinct in regards to the period of time spent in this paintings, it's attainable to be certain concerning the date of its inception. In 1984, in the course of study within the archive of the École polytechnique, my cognizance was once attracted to the way the large rupture that came about in 1811―precipitating the swap again to the factitious procedure and exchanging the restrict technique via the tactic of the quantités infiniment petites―significantly altered the instructing of research at this primary glossy establishment of upper schooling, an establishment initially based as a castle of the analytic strategy.

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Extra resources for Conflicts between generalization, rigor, and intuition: number concepts underlying the development of analysis in 17th-19th century France and Germany

Example text

Newton and Leibniz, however, extended their investigations to transcendental functions. The problems of how to develop transcendental functions into series and the latter’s impact on the meaning of the foundational concepts were to become the principal focus for research into analysis. In his Method of fluxions, Newton introduced the distinction between independent and dependent (variable) quantities, as quantitas correlata and quantitas relata. In Leibniz’s manuscripts, the term function is found for the first time in 1673, for the relation between ordinates and abscissae of a curve given by an equation.

2. Negative Numbers: Antiquity 37 negative quantities being implied. Rather, Diophantus rejected negative solutions, just as he did irrational or complex ones, avoiding roots of such kind by restricting the equations further, when necessary. There is only one problem in which Diophantus obtained an equation with a negative solution. ” He therefore felt compelled to change his original hypotheses (Sesiano 1985, 106). Hitherto, just a small part of the surviving texts of Arabic mathematicians have been evaluated.

It must be noted that with Arbogast, just as with many contemporary mathematicians, the concept “loi de continuité” occurs in a twofold meaning: both as the analytic (formulaic) expression of a curve or a part of it, and as the conceptual content of the function’s property of continuity. Steps toward conceptually defining the continuity of functions could not be taken before the relationship between these two meanings had been clarified. One of the conditions for this was to abandon the hitherto prevailing epistemology of mathematics by adopting an algebraic–analytic view of mathematical objects, a move that conferred a more fundamental status on functions than on the curves they represent.

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Conflicts between generalization, rigor, and intuition: number concepts underlying the development of analysis in 17th-19th century France and Germany by Gert Schubring

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