Timeline for Are limits decidable? Should definitions be decidable? [closed]
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2015 at 8:29 | history | closed |
Jeremy Rickard Andrés E. Caicedo Chris Godsil Andy Putman Alex Degtyarev |
Not suitable for this site | |
| Aug 5, 2015 at 6:04 | comment | added | Terry Tao | As for a more computable notion of a limit, you may be interested in the concept of metastability, which I discuss at terrytao.wordpress.com/2007/05/23/… | |
| Aug 5, 2015 at 5:55 | comment | added | Terry Tao | However, one can informally interpret "existential" axioms (such as the axiom of choice or the least upper bound axiom) from a "computational" perspective as providing various "oracles" that extend a base computational model. I discuss this (rather non-rigorously) at terrytao.wordpress.com/2010/03/19/… | |
| Aug 5, 2015 at 5:52 | comment | added | Terry Tao | Formally, mathematics is founded on axiomatic systems, rather than on computational models; the Church-Turing thesis does not apply to (say) structures of ZFC. In an axiomatic system, a term is well defined so long as it provably has a unique interpretation for all admissible choices of parameters. Computability of this interpretation would be a desirable bonus if available, but is not necessary in order to usefully take advantage of a mathematical definition. | |
| Aug 5, 2015 at 5:49 | history | edited | Daniel Mansfield | CC BY-SA 3.0 |
made title match the updated question
|
| Aug 5, 2015 at 5:37 | comment | added | Daniel Mansfield | Thanks for helping me to grow my question. I've split this into two parts: first I'd like to know if there is a decidable version of $\lim$. For the second question I'm interested in people's opinion on what constitutes a definition. | |
| Aug 5, 2015 at 5:27 | history | edited | Daniel Mansfield | CC BY-SA 3.0 |
improved question
|
| Aug 5, 2015 at 4:38 | comment | added | Robert Israel | Actually, when you look closely at elementary analysis, lots of things are undecidable. For example, you might consider Richardson's Theorem en.wikipedia.org/wiki/Richardson%27s_theorem which says that, for a very natural class of expressions, it's impossible to tell if they are equal to $0$. | |
| Aug 5, 2015 at 4:03 | comment | added | Noah Schweber | Now there is a question, but I don't understand what it means. What would you consider a satisfactory answer? | |
| Aug 5, 2015 at 3:59 | history | edited | Daniel Mansfield | CC BY-SA 3.0 |
made into more of a question
|
| Aug 5, 2015 at 2:04 | review | Close votes | |||
| Aug 5, 2015 at 8:29 | |||||
| Aug 5, 2015 at 1:48 | comment | added | Jeremy Rickard | I'm voting to close this as off-topic because MathOverflow is not a discussion forum and this post is seeking to start a discussion rather than asking a question. | |
| Aug 5, 2015 at 1:16 | answer | added | Bjørn Kjos-Hanssen | timeline score: 3 | |
| Aug 5, 2015 at 0:31 | history | asked | Daniel Mansfield | CC BY-SA 3.0 |