Timeline for What practical applications does set theory have?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2022 at 15:14 | comment | added | Pablo H | In modern Mathematics (at least the one I studied just before year 2000), everything is a set (e.g. real numbers given by model such as Dedekind cuts), or a set plus axioms (e.g. numbers given as sets plus axioms). Functions are relations, which are (sub)sets. Algebraic structures, spaces, etc. are sets. The only exception I know of is categories, which are not sets. | |
| Aug 5, 2021 at 7:22 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Apr 11, 2019 at 13:08 | comment | added | user44143 | @QiaochuYuan, "it's fair to say the development of general relativity"...did not require much topology or the language of set theory. The Einstein papers are now online, e.g. einsteinpapers.press.princeton.edu/vol6-trans/129; the math Einstein used was mostly Riemann's curvature tensor and Ricci's tensor calculus, fully coordinatized. | |
| Jun 13, 2015 at 5:46 | comment | added | user21820 | @QiaochuYuan: Oh okay I had interpreted your answer differently. Thanks for clarifying! | |
| Jun 13, 2015 at 4:28 | comment | added | Qiaochu Yuan | @user21820: I assume nothing of the sort. I'm making a purely descriptive claim: the way people do in fact understand topology is via a set-theoretic description of topological spaces. There's a very interesting conversation to be had about alternative approaches, such as those involving type theory, but I'm not making any claims about those. | |
| Jun 12, 2015 at 4:18 | comment | added | user21820 | I have a problem with this answer. It assumes that we cannot understand things like infinite sums without set theory. Why is set theory superior to alternatives like type theory? To me it is like saying that without programming language we cannot have useful software, and therefore we should learn assembly language. | |
| Dec 1, 2013 at 10:36 | comment | added | Delio Mugnolo | @Harry Gindi - well, even more down to earth: without infinite sums it would not be possible to talk about fourier series, fourier transforms, hilbert spaces. not to mention quantum mechanics. | |
| Jan 8, 2010 at 3:24 | vote | accept | user2929 | ||
| Jan 1, 2010 at 1:40 | comment | added | Harry Gindi | Another example for your second point: Topology changes infinite sums from nonsense into legitimate mathematical objects because it allows us to talk about convergence. This is exceedingly clear when one studies things like the I-adic topology on a ring R or appropriate R-module. | |
| Jan 1, 2010 at 1:34 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
added 581 characters in body
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| Jan 1, 2010 at 1:23 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
added 580 characters in body
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| Jan 1, 2010 at 0:41 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |