Timeline for Are there more rational numbers than integers?
Current License: CC BY-SA 2.5
21 events
| when toggle format | what | by | license | comment | |
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| Jun 8 at 15:46 | answer | added | Anixx | timeline score: 0 | |
| Oct 24, 2022 at 10:24 | comment | added | Julius Hamilton | I think this is one of the best posts on Math SE, a very intuitive question often overlooked | |
| Sep 2, 2021 at 14:55 | answer | added | Samuel M. A. Luque | timeline score: 0 | |
| Feb 11, 2015 at 18:57 | history | protected | Asaf Karagila♦ | ||
| Feb 3, 2014 at 19:36 | comment | added | Cruncher | @Steve314 This is why Qiaochu gave successful ad absurdum reasoning. He's saying that by the reasoning that you gave, you could also prove that there are more integers than integers, which is clearly false. Ergo the original reasoning is incorrect. | |
| Jan 5, 2014 at 16:56 | history | edited | Andrés E. Caicedo |
edited tags
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| Apr 11, 2013 at 0:48 | comment | added | Noah Snyder | You may find helpful some of the answers to the similar question math.stackexchange.com/questions/398 | |
| Jul 31, 2010 at 21:45 | comment | added | user510 | @ShreevatsaR - yes, that's my point. Why should "size" mean "cardinality of the set"? Simple answer - it's the only way to get a meaningful answer. But if you approach the issue worrying about curves and areas, it's hard not to see a different sense of the word "size". | |
| Jul 31, 2010 at 21:32 | comment | added | ShreevatsaR | Re edit: There's a confusion here between two distinct concepts of cardinality and measure. The cardinality of the set of points on a one-metre line segment and on a two-metre line is the same, but they have different measure (length, in this case). Similarly, the Hilbert space-filling curve fills all the points, but being a curve, it has measure 0 relative to the square it fills (it has length, but no area). The confusion arises because "size" is used loosely to refer to either concept. | |
| Jul 31, 2010 at 21:22 | history | edited | user510 | CC BY-SA 2.5 |
Extra context - Hilbert curves
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| Jul 31, 2010 at 20:51 | comment | added | user510 | @Qiaochu Yuan - that had occured to me, but I thought trying to argue that there are more integers than integers or visa versa was well down the road to insanity ;-) | |
| Jul 31, 2010 at 20:26 | answer | added | Niel de Beaudrap | timeline score: 6 | |
| Jul 31, 2010 at 20:17 | comment | added | Qiaochu Yuan | Second to last paragraph: you can also argue that there are potentially infinite integers for every single integer. | |
| Jul 31, 2010 at 20:11 | answer | added | mau | timeline score: 3 | |
| Jul 31, 2010 at 20:09 | answer | added | vanden | timeline score: 2 | |
| Jul 31, 2010 at 20:08 | vote | accept | CommunityBot | ||
| Jul 31, 2010 at 20:08 | vote | accept | CommunityBot | ||
| Jul 31, 2010 at 20:08 | |||||
| Jul 31, 2010 at 20:04 | answer | added | Lucky | timeline score: 0 | |
| Jul 31, 2010 at 20:01 | answer | added | Jason DeVito - on hiatus | timeline score: 26 | |
| Jul 31, 2010 at 19:53 | history | edited | Isaac | CC BY-SA 2.5 |
edited tags; edited title
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| Jul 31, 2010 at 19:49 | history | asked | user510 | CC BY-SA 2.5 |