Timeline for Direct proof of irrationality?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2022 at 13:20 | history | edited | Bill Dubuque | CC BY-SA 4.0 |
added 211 characters in body
|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jul 16, 2010 at 17:22 | history | edited | Bill Dubuque | CC BY-SA 2.5 |
added 21 characters in body
|
| Jul 15, 2010 at 22:39 | comment | added | Bill Dubuque | Yes, of course there are many variations. But they are all mechanically derivable from the more conceptual ideal-based proofs, as I explain at length in the sci.math linked indirectly above. Thus they're all essentially equivalent and the key idea goes way back to Dedekind. I could easily write a program that could generate all of the known "elementary" proofs by unwinding the conceptual proofs, eliminating higher-order concepts like ideals, modules, and directly inlining lemmas, etc. Such elementary proofs are not novel in any way. | |
| Jul 15, 2010 at 16:47 | comment | added | Bill Dubuque | But every proof does the same at some point - even if it's far down the line in some chain of lemmas, e.g. see the Gower's link above. | |
| Jul 15, 2010 at 16:34 | comment | added | Rasmus | Your theorem is neat, though. | |
| Jul 15, 2010 at 16:31 | comment | added | Rasmus | So your proof of irrationality of $\sqrt{2}$ is follows: Assume $\sqrt{2}$ was rational. Then my theorem implies that $\sqrt{2}$ is integral, which is obviously impossible since no integer squares to $2$. QED. But this is a proof by contradiction isn't it? | |
| Jul 15, 2010 at 16:16 | history | edited | Bill Dubuque | CC BY-SA 2.5 |
added 6 characters in body; deleted 2 characters in body
|
| Jul 15, 2010 at 16:01 | history | edited | Bill Dubuque | CC BY-SA 2.5 |
added 12 characters in body
|
| Jul 15, 2010 at 15:57 | comment | added | RubeRad | That's really slick too; I'll have to make some time to read the link... | |
| Jul 15, 2010 at 15:57 | vote | accept | RubeRad | ||
| Jul 15, 2010 at 15:45 | history | edited | Bill Dubuque | CC BY-SA 2.5 |
edited body
|
| Jul 15, 2010 at 15:34 | history | answered | Bill Dubuque | CC BY-SA 2.5 |