Questions tagged [infinitesimals]
The infinitesimals tag has no usage guidance.
11
questions
1
vote
0
answers
44
views
infinitesimal generators for G/G/1 queue
I read the infinitesimal generator for the M/M/1 queue and thought to generalize to the G/G/1 queue. More specifically, though the queue length process is not Markovian anymore, we could consider an ...
- 173
23
votes
1
answer
2k
views
Has anything (other than what is in the obituary written 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,...
- 5,785
1
vote
1
answer
352
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 ...
- 8,368
14
votes
2
answers
2k
views
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 ...
- 12.4k
12
votes
1
answer
343
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. ...
- 16.2k
1
vote
0
answers
115
views
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 ...
- 8,368
3
votes
0
answers
167
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 $\...
- 8,368
21
votes
3
answers
2k
views
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 ...
- 12.4k
4
votes
2
answers
416
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....
- 12.4k
3
votes
1
answer
204
views
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 ...
- 29.5k
9
votes
3
answers
2k
views
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:
...
- 10.2k