Timeline for How are mathematical objects defined from an ultrafinitist perspective?
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9 events
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| Jan 26, 2013 at 23:29 | comment | added | Russell Easterly | I am not sure one can talk about lines and circles in an ultrafinite theory. The set of points equidistant from some point (using some measure) will always be a finite set. I have studied graphs where the number of points equidistant from the origin oscillates between 3*r and 4*r depending on the radius. It is easy to come up with graphs where the average ratio of equidistant points to radius approaches Pi for large r. | |
| Jan 26, 2013 at 15:54 | answer | added | user21349 | timeline score: 7 | |
| Jan 26, 2013 at 6:59 | history | edited | Kaveh |
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| Jul 18, 2011 at 7:57 | comment | added | Kaveh | @Todd, :) also here: scottaaronson.com/blog/?p=103 or even maybe on FOM mailing list. | |
| Jul 18, 2011 at 6:49 | comment | added | Todd Trimble | @Kaveh: I told the story here: mathoverflow.net/questions/44208/… | |
| Jul 18, 2011 at 6:44 | comment | added | Kaveh | @Daniel Mehkeri, I remember reading somewhere that one of the famous mathematicians and logicians argued with Alexander Esenin-Volpin about it. At the end he decided to try to find what is the largest natural number that Alexander Esenin-Volpin was ready to admit that it exists. After sometime the famous mathematicians noticed that this is not going to work, because as the numbers increased Alexander Esenin-Volpin waited proportionally more time before replying with yes, he accepts that number exists. | |
| Jul 18, 2011 at 4:52 | comment | added | Daniel Mehkeri | @Zen Harper: I am not an ultrafinitist either, but that sounds more like a finitist viewpoint. As I understand ultrafinitism, it wouldn't even allow "potential infinity". Troelstra and van Dalen (Constructivism in Mathematics) succinctly summarise ultrafinitism as rejecting the idea that we can view 2^1024 as a sequence of units, even in principle. I have argued with a few people calling themselves ultrafinistists, I think they generally accept that, and those (one?) that don't will still agree that "potential infinity" is not kosher. | |
| Jul 18, 2011 at 3:05 | comment | added | Zen Harper | I'm not an ultrafinitist, but I would imagine they would say that the whole idea of considering an infinite set is misguided according to their philosophy; "potentially-infinite" (as in, unbounded/unlimited) is OK, but a completed infinite set is not. | |
| Jul 18, 2011 at 2:15 | history | asked | teil | CC BY-SA 3.0 |