Comments on: Soft analysis, hard analysis, and the finite convergence principle
https://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 Feb 2017 05:54:41 +0000hourly1http://wordpress.com/By: Hard analysis, soft analysis
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-477259
Fri, 27 Jan 2017 14:18:56 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-477259[…] I was trained as a bird, but I’ve become more of a frog over time. Of course these categories are not exclusive. Frogs sometimes act as birds and vice versa. The categories of hard and soft analysis are not exclusive either. See Terry Tao’s article on relating hard and soft analysis. […]
]]>By: Hilbert’s Curve, and the usefulness of infinite results in a finite world | Coding Tweaks
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-475024
Wed, 14 Dec 2016 16:28:45 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-475024[…] Soft analysis, hard analysis, and the finite convergence principle c++ programs […]
]]>By: Hilbert’s Curve, and the usefulness of infinite results in a finite world | Coding Craze
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-474999
Tue, 13 Dec 2016 02:40:44 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-474999[…] Soft analysis, hard analysis, and the finite convergence principle c++ programs […]
]]>By: The logarithmically averaged Chowla and Elliott conjectures for two-point correlations; the Erdos discrepancy problem | What's new
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-459432
Sat, 19 Sep 2015 00:46:38 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-459432[…] at some point one must reach a metastable region (cf. the finite convergence principle discussed in this previous blog post), within which very little mutual information can be shared between the sequence and the graph . […]
]]>By: O intâlnire cu informatica teoretică românească: FMI@150 Ziua I | Isarlâk
https://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
https://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
https://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
https://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
https://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
https://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“) […]
]]>