Timeline for Intermediate value theorem on computable reals
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2021 at 19:03 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
|
| Oct 12, 2021 at 17:30 | history | edited | Paul Taylor |
added newly created tag
|
|
| Jan 1, 2010 at 20:15 | answer | added | Paul Taylor | timeline score: 13 | |
| Dec 22, 2009 at 0:10 | answer | added | Reid Barton | timeline score: 10 | |
| Dec 21, 2009 at 23:40 | answer | added | Andrej Bauer | timeline score: 20 | |
| Dec 17, 2009 at 6:49 | vote | accept | Jason Orendorff | ||
| Dec 16, 2009 at 18:19 | answer | added | Joel David Hamkins | timeline score: 31 | |
| Dec 15, 2009 at 17:51 | comment | added | Jason Orendorff | I can see that there's an existential quantifier in the IVT, and if it is to be proven, then that has to come from somewhere. If you write out the proof for the reals, that quantifier clearly comes from invoking the least upper bound property. If it's obvious that one just can't get an existential quantifier on the computable reals, then that's the piece I'm missing (and, in that case, sorry for the dumb question!) | |
| Dec 15, 2009 at 17:45 | comment | added | Jason Orendorff | Gabriel Benamy: Like this-- "If a continuous computable function f maps the computable reals in the interval [x1, x2] to computable reals, with f(x1)=y1 and f(x2)=y2, then for any computable number yc between y1 and y2, there is some computable number xc between x1 and x2 such that the function at f(xc)=yc." (Continuity is defined the same for the computable reals as for the reals, in case that's the difficulty.) | |
| Dec 15, 2009 at 17:37 | comment | added | Jason Orendorff | Qiaochu Yuan: Thanks for the link. I'm not interested in adopting intuitionist logic; an existence proof would satisfy me. | |
| Dec 15, 2009 at 16:59 | answer | added | Neel Krishnaswami | timeline score: 7 | |
| Dec 15, 2009 at 16:56 | comment | added | Gabriel Benamy | I'm afraid I don't understand your question. The IVT says that if a continuous function has range (y1,y2) over some interval (x1,x2) then for any yc between y1 and y2, there is some xc between x1 and x2 such that the function at f(xc) = yc. I don't understand how this is meant to be extended to the computable reals... | |
| Dec 15, 2009 at 16:48 | comment | added | Qiaochu Yuan | Have you read en.wikipedia.org/wiki/… already? | |
| Dec 15, 2009 at 16:42 | history | asked | Jason Orendorff | CC BY-SA 2.5 |