Comments on: Ultrafilters, nonstandard analysis, and epsilon management
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoSun, 29 May 2016 05:05:27 +0000hourly1http://wordpress.com/By: Terence Tao
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-468004
Wed, 27 Apr 2016 16:44:44 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-468004I found Goldblatt’s “lectures on the hyperreals” to be a good introduction.
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https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-467995
Wed, 27 Apr 2016 13:56:57 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-467995Dear Sir , i want to do ph.d in non standard analysis. can you tell me some standard books on non standard analysis
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https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-467791
Sun, 17 Apr 2016 23:18:45 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-467791In this link we can see a new approach to nonstandard analysis without using the model theory. https://hal.inria.fr/hal-01248379/
]]>By: Sumfree sets in groups | What's new
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-466846
Fri, 11 Mar 2016 16:55:16 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-466846[…] of the problem in order to keep the complexity of the argument at a reasonable level (cf. my previous blog post on this topic). One drawback of doing so is that we have no effective bounds for the implied […]
]]>By: What is Gauge? | The Conscience of A Libertarian
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-461918
Sun, 15 Nov 2015 23:04:23 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-461918[…] infinitesimals such as dx. (There are ways to make the use of infinitesimals rigorous, such as non-standard analysis, but this is not the focus of my post […]
]]>By: A nonstandard analysis proof of Szemeredi’s theorem | What's new
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-457534
Tue, 21 Jul 2015 04:23:02 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-457534[…] extension” component of the argument). But the proof was still quite messy. However, as discussed in this previous blog post, messy finitary proofs can often be cleaned up using nonstandard analysis. Thus, there should be a […]
]]>By: Ultrafilters – I. the Stone-Čech compactification | the capacity to be alone
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-452746
Fri, 06 Mar 2015 02:08:29 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-452746[…] Tao’s fantastic voting analogy for ultrafilters is one of my favorite intuitions I’ve ever read. After sitting through a lecture of said […]
]]>By: Hindman’s Theorem | Finite Playground
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-324626
Mon, 05 May 2014 23:36:09 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-324626[…] reading the posts on ultrafilters by Terry Tao [1,2], I find the following result […]
]]>By: Ultraproducts as a Bridge Between Discrete and Continuous Analysis | What's new
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-255862
Sun, 08 Dec 2013 00:06:07 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-255862[…] has as a preferred candidate, and the ultrafilter is used as the election protocol. (See this previous post for further discussion of this […]
]]>By: What does Kadison-Singer have to do with Quantum Mechanics? | tcs math - some mathematics of theoretical computer science
https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-237439
Thu, 04 Jul 2013 18:05:45 +0000http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/#comment-237439[…] identified with , the Stone-Cech compactification of the naturals. See Terry Tao’s notes on ultafilters and Stone-Cech […]
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