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Questions tagged [infinitesimals]

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21
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Has anything (other than what is in the obituary witten by M. Noether) survived of Paul Gordan's defense of infinitesimals?

Question. Has anything other than what can be guessed from this obituary written by Max Noether survived of the 'defense' of infinitesimals that Paul Gordan gave in his doctoral disputation on March 1,...
1
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1answer
338 views

Has anybody proposed such a generalization of integration?

Has anybody ever proposed a generalization of integration in which an integral of a function that has non-zero values only on a countable set produces non-zero (but maybe infinitesimal) result? For ...
15
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2answers
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Fermat's opponents

It is well known among historians of Fermat that, while his technique of adequality prepared the ground for the general framework later developed by Leibniz and Newton, Fermat himself gave very little ...
12
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1answer
328 views

Multiplicative infinitesimals in q-analogs?

Risking to be downvoted, here is a very lightweight question. In various fields - say, algebraic geometry, nonstandard analysis, synthetic differential geometry - infinitely small quantities, i. e. ...
1
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0answers
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Obtaining graphics of functions in non-standard analysis [closed]

In the context of $R(\varepsilon)$ or more broad fields, Levi-Civita field or $No(\omega_1)$, how can we obtain the graphics of functions on the infinitesimal range? For instance, it is alleged that ...
3
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0answers
165 views

Analysing functions on zero-length intervals and super-small values

Suppose a function that has a pole in $x=0$: Here we see the graphic of the real part of the Gamma function. As we can see on it, there is a vertical line at $x=0$ that comes from $-\infty$ to $\...
21
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3answers
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Felix Klein on mean value theorem and infinitesimals

This is a reference request prompted by some intriguing comments made by Felix Klein. In 1908, Felix Klein formulated a criterion of what it would take for a theory of infinitesimals to be ...
3
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2answers
387 views

Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book Robinson, A.; Laurmann, J. A. Wing theory....
3
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1answer
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Can elements of Weil algebras be detected by maps into truncated symmetric algebras?

Recall that a Weil algebra is a finite-dimensional real unital algebra that admits exactly one homomorphism to R. Such algebras form the basis of the Weil approach to differential geometry, pioneered ...
6
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3answers
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Nontrivial trivial integrals

I posted this question to stackexchange and after 24 hours it's got five votes and no answers, so let's see if mathoverflow can say more than that. Consider two propositions in geometry: ...