Comments on: Soft analysis, hard analysis, and the finite convergence principle
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoTue, 21 Oct 2014 18:57:01 +0000hourly1http://wordpress.com/By: O intâlnire cu informatica teoretică românească: FMI@150 Ziua I | Isarlâk
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-243296
Fri, 30 Aug 2013 20:20:36 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-243296[…] de faptul că domeniul este unul interesant vă puteți convinge de exemplu citind această discuție pe blogul lui Terry Tao. Ar fi interesant de văzut câte din lucrurile din acest domeniu pot fi automatizate. Impresia pe […]
]]>By: Topological order for mixed states | Tobias J. Osborne's research notes
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-231779
Wed, 29 May 2013 20:40:28 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-231779[…] The definition provided by Hastings is much closer in spirit with this second definition. (It’s worth noting that by working in the infinite lattice size limit we can avoid lots of s and s; we can make our soft analysis definition a hard analysis definition if we like in the standard way.) […]
]]>By: Analogies between finitary and infinitary math | Abstract Art
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230426
Mon, 20 May 2013 15:04:02 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230426[…] [1.3] Soft analysis, hard analysis, and the finite convergence principle […]
]]>By: Frank
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230111
Sat, 18 May 2013 05:28:15 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230111Dear professor:
Sorry for my ignorance. In my opinion, the proof of the part (the infinite convergence principle implying the finite convergence principle) is imperfect. The compactness or completeness of the real line might as well be avoided, since the theorem, i.e, the monotone sequence of rational numbers on is Cauchy as well. The compactness of depends on that, I think.
]]>By: andrescaicedo
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230025
Fri, 17 May 2013 19:50:42 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230025Jennifer Chayes’s link is outdated. The current link should be http://research.microsoft.com/en-us/um/people/jchayes/

[Corrected, thanks - T.]

]]>By: Bird’s-eye views of Structure and Randomness (Series) | Abstract Art
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-228784
Sat, 11 May 2013 06:05:12 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-228784[…] Analogies between finitary and infinitary math (adapted from “Soft analysis, hard analysis and the finite convergence principle“) […]
]]>By: The spectral proof of the Szemeredi regularity lemma « What’s new
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-199142
Tue, 04 Dec 2012 01:35:50 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-199142[...] with for all . Applying (3) and the pigeonhole principle (or the finite convergence principle, see this blog post), we can find such [...]
]]>By: The three Moirai, continued « chorasimilarity
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-195459
Fri, 23 Nov 2012 11:57:30 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-195459[...] Now the construction is finished, let us let the Moirai to do their job. Finally, I shall recall my real goal, which I have never forgot. The real goal is to pass from understanding of the power of this lambda calculus sector of graphic lambda calculus to the real deal, called “computing with space”, namely to understand space from a computational perspective, not as a given receptacle, but as a small list of procedures along with some impossible to verify assertions (like that we may rescale indefinitely space), see “emergent algebras”, which can always be eliminated a posteriori, by a kind of finitization procedure. [...]
]]>By: Walsh’s ergodic theorem, metastability, and external Cauchy convergence « What’s new
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-185892
Thu, 25 Oct 2012 18:10:45 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-185892[...] which is useful in situations in which one does not expect a uniform convergence rate; see this previous blog post for some discussion of metastability. When interpreted in a finitary setting, this concept requires [...]
]]>By: Functional Analysis – Introduction. Part II « Noncommutative Analysis
http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-176965
Mon, 01 Oct 2012 09:02:42 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-176965[...] of substance, which applies to concrete cases in analysis, that does not involve some kind of hard analysis, some epsilonaustics, some sweat. In our example, the hard analysis comes in the proof of the [...]
]]>