bio | website | u.cs.biu.ac.il/~katzmik |
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visits | member for | 1 year, 11 months |
seen | Aug 24 at 12:51 | |
stats | profile views | 1,919 |
Interesting questions:
Papers that debunk common myths in the history of mathematics
Sep 24 |
awarded | Autobiographer |
Aug 22 |
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natural map from $H^3(BG,\mathbb{Z})$ to $H^3(\underline E G,\mathbb{Z})$?
So the answer is affirmative. |
Aug 20 |
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What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?
@MattF., first of all thanks for your answer. As far as the question title is concerned, I think the change is fine. Arguably "constructive" can be used in the sense of "relying on an intuitionistic logic". The identification of "constructive" and "computational" is one of the cornerstones of Bishop's approach but one may be allowed to hold alternative opinions. For an analysis of Bishop's ideology see arxiv.org/abs/1110.5456 In fact your comment could be the subject of a separate question if you wish to pursue it. |
Aug 19 |
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Survey of the history of calculus?
added 44 characters in body |
Aug 18 |
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What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?
Regarding uniform continuity: as I recall the proof in van Dalen--Troelstra that the maximal value exists depends on the function being uniformly continuous on the interval rather than merely continuous. Is this otherwise in SIA? |
Aug 17 |
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What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?
Thanks Paul this is terrific. I should have clarified that I had uniform continuity in mind. This still admits of counterexamples as you know. Also, I was looking for a maximum ($x$) rather than a maximal value ($y$). |
Aug 15 |
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Local geodesics in uniquely geodesic spaces
@Teri, Perhaps you should reformulate your question accordingly. |
Aug 13 |
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Salvaging Leibnizian formalism?
@Andrej, please see the related post mathoverflow.net/questions/178438/… |
Aug 13 |
asked | What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis? |
Aug 13 |
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Salvaging Leibnizian formalism?
Steve, the problem with this approach to infinitesimals is that it does not capture the full strength of Robinson's transfer principle. This apparently applies to the other answer as well since the reliance on intuitionistic logic undermines certain arguments that Robinson's transfer principle does apply to. |
Aug 13 |
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Salvaging Leibnizian formalism?
added 848 characters in body; edited tags |
Aug 12 |
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Local geodesics in uniquely geodesic spaces
books.google.co.il/… |
Aug 12 |
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Local geodesics in uniquely geodesic spaces
No, $q$ is the "last" point with a unique minimizer. |
Aug 12 |
answered | Local geodesics in uniquely geodesic spaces |
Aug 12 |
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Finiteness as a motivation for compactness
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Aug 12 |
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Salvaging Leibnizian formalism?
I finally got a chance to look up Kolar et al. This seems to focus on naturality in differential geometry and it is hard to see how this relates to developing a framework for infinitesimals. Perhaps @Peter Michor could comment? |
Aug 12 |
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Finiteness as a motivation for compactness
The second link doesn't get you anywhere either without a password. Can you include a direct link to jstor instead of your university's proxy? |
Aug 12 |
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Salvaging Leibnizian formalism?
edited tags |
Aug 12 |
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Salvaging Leibnizian formalism?
... a framework as well. @S. |
Aug 12 |
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Salvaging Leibnizian formalism?
... of variables. Also the center of curvature of a plane curve at a point should literally "=" the intersection of a pair of infinitely close normals (a definition right out of Cauchy, by the way). Infinitesimal calculations in Gauss and Riemann should be literally true, e.g., formula for curvature in terms of second order differentials. As you may know, Lie's original approach to Lie algebras was by means of infinitesimal displacements in the Lie group. This can be done by means of elementary nilpotent infinitesimals (this does not require Lawvere's framework), but it should fit into such... |