Timeline for Axiom of choice and convergence
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2012 at 12:11 | comment | added | Jean-Luc Bouchot | Found what I was looking for! (my question was a bit far away, I have to admit!): en.wikipedia.org/wiki/Specker_sequence | |
| Feb 1, 2012 at 11:55 | comment | added | Jean-Luc Bouchot | Perfect! Thanks a lot. Do you have any pointers to those things? | |
| Feb 1, 2012 at 11:46 | comment | added | Emil Jeřábek | I should stress that the reals are constructively complete, in the sense that every Cauchy sequence converges. The nonconstructive part in the monotone convergences theorem is to show that a bounded monotone sequence is Cauchy. | |
| Feb 1, 2012 at 11:25 | comment | added | Emil Jeřábek | Constructivism rejects the law of excluded middle. And indeed, it is not constructively provable that every bounded monotone sequence has a limit. This is closely connected to the fact that there are computable monotone sequences whose limit is not computable. | |
| Feb 1, 2012 at 11:13 | comment | added | Jean-Luc Bouchot | I guess that's it. But I can remember reading a couple of month ago some kind of non convergent sequence on the real line. Could it be that constructivsm reject something at one point, and therefore manage to exhibit such a sequence? | |
| Feb 1, 2012 at 11:10 | vote | accept | Jean-Luc Bouchot | ||
| Feb 1, 2012 at 10:56 | history | answered | Valerio Capraro | CC BY-SA 3.0 |