Newest at the top
| 2025-02-26 11:00:22 +0100 | bilegeek | (~bilegeek@2600:1008:b06e:701b:8c92:bcff:3789:c22c) (Quit: Leaving) |
| 2025-02-26 10:59:08 +0100 | <tomsmeding> | https://ncatlab.org/nlab/show/concept+with+an+attitude |
| 2025-02-26 10:59:04 +0100 | <Leary> | I'm still not sure what the original statement is supposed to be. f and g are partial functions with opposite co/domains and the property that each is total on the other's range? |
| 2025-02-26 10:58:01 +0100 | <[exa]> | anyway yeah, I'd say the original definiton would need a bit more of a spirit to it to actually spawn a useful name |
| 2025-02-26 10:57:26 +0100 | <[exa]> | ah well okay in math that could cause issues, I see |
| 2025-02-26 10:57:24 +0100 | <tomsmeding> | but if you already have the types of f and g, there's nothing more to specify! |
| 2025-02-26 10:57:10 +0100 | <[exa]> | f.f doesn't type |
| 2025-02-26 10:56:17 +0100 | <tomsmeding> | if it's just "f . g", then it's weaker; if you also include "f . f", then it's stronger |
| 2025-02-26 10:55:59 +0100 | <tomsmeding> | depends on what compositions you mean when you say "compositions of f and g" |
| 2025-02-26 10:55:55 +0100 | <[exa]> | so I'd say it's the same |
| 2025-02-26 10:55:40 +0100 | <[exa]> | the totality of the composition implies exactly the domain-is-a-superset property that was requested, and I just run it in both directions |
| 2025-02-26 10:54:41 +0100 | <tomsmeding> | that's not quite the same statement, is it? |
| 2025-02-26 10:54:37 +0100 | <cheater> | i don't like puzzle definitions |
| 2025-02-26 10:54:20 +0100 | <[exa]> | cheater: you can just say that compositions of f and g are total |
| 2025-02-26 10:52:11 +0100 | <cheater> | that sounds like something out of control theory. |
| 2025-02-26 10:51:20 +0100 | merijn | (~merijn@77.242.116.146) merijn |
| 2025-02-26 10:51:04 +0100 | xff0x | (~xff0x@fsb6a9491c.tkyc517.ap.nuro.jp) (Ping timeout: 272 seconds) |
| 2025-02-26 10:49:13 +0100 | <tomsmeding> | you can call it a "back-and-forth" |
| 2025-02-26 10:48:39 +0100 | <cheater> | if no such thing is described then i shall coin that as a speculative function pair (or tuple for a more complex graph) |
| 2025-02-26 10:47:02 +0100 | tromp | (~textual@2a02:a210:cba:8500:b949:287e:6bbd:873b) |
| 2025-02-26 10:46:18 +0100 | <cheater> | no, they have no such property as stated |
| 2025-02-26 10:45:55 +0100 | <cheater> | i think that's interesting enough. |
| 2025-02-26 10:45:51 +0100 | <tomsmeding> | if f and g are continuous and bijective, then they are homeomorphisms, for example |
| 2025-02-26 10:45:48 +0100 | zmt01 | (~zmt00@user/zmt00) (Ping timeout: 252 seconds) |
| 2025-02-26 10:45:44 +0100 | <cheater> | the only property is that if you start in one set, you can infinitely go between the two sets using f and g. possibly ending at some limit element or not. |
| 2025-02-26 10:45:02 +0100 | <tomsmeding> | cheater: if the functions have some equation relating them, then there may be appropriate terminology, but without any equation relating them, I don't think there's a word for this |
| 2025-02-26 10:44:34 +0100 | <cheater> | f and g are connected by the property i listed above: they are total on sets that contain each other's codomains |
| 2025-02-26 10:44:02 +0100 | <tomsmeding> | Leary: That's fair |
| 2025-02-26 10:43:42 +0100 | <tomsmeding> | (and that's usually modelled as a total function to Y + 1) |
| 2025-02-26 10:43:42 +0100 | <cheater> | they are total on their domains, but their domains don't have to line up like they do in my hypothesis |
| 2025-02-26 10:43:38 +0100 | kaskal | (~kaskal@84-115-238-111.cable.dynamic.surfer.at) kaskal |
| 2025-02-26 10:43:31 +0100 | <tomsmeding> | it's the concept of a "partial function" that needs explicit note |
| 2025-02-26 10:43:10 +0100 | <tomsmeding> | functions are total by default in mathematics |
| 2025-02-26 10:43:04 +0100 | <tomsmeding> | those are just a pair of functions |
| 2025-02-26 10:42:56 +0100 | <tomsmeding> | I don't see any connection between f and g here |
| 2025-02-26 10:42:55 +0100 | <cheater> | a pair of total functions between two sets going in opposite directions |
| 2025-02-26 10:42:40 +0100 | swamp_ | (~zmt00@user/zmt00) zmt00 |
| 2025-02-26 10:42:37 +0100 | <cheater> | yes |
| 2025-02-26 10:42:32 +0100 | <tomsmeding> | cheater: so then that first formula says that f is total? I.e. it returns a result for every x? |
| 2025-02-26 10:42:07 +0100 | <Leary> | Multiple terminologies can coexist. I also don't consider the language around /releases/ to conflict with the language for the version components. |
| 2025-02-26 10:41:56 +0100 | <cheater> | tomsmeding: yes. that's a shorthand. |
| 2025-02-26 10:41:16 +0100 | <tomsmeding> | though actually the GHC wiki terminology is rather close to this |
| 2025-02-26 10:40:32 +0100 | merijn | (~merijn@77.242.116.146) (Ping timeout: 244 seconds) |
| 2025-02-26 10:40:25 +0100 | <tomsmeding> | Leary: Well, then the GHC user guide disagrees, and the GHC wiki contests the nuance. :P |
| 2025-02-26 10:39:43 +0100 | <Leary> | tomsmeding: In line with HLS: 9.12 ~ major (version (numbers)); 1 ~ minor (version (number)). At least that's the language I would use; I doubt there's an official decree. |
| 2025-02-26 10:37:22 +0100 | <tomsmeding> | or something |
| 2025-02-26 10:37:13 +0100 | <tomsmeding> | perhaps you meant "\A x \in X \E y (f(x) = y)"? |
| 2025-02-26 10:36:59 +0100 | lxsameer | (~lxsameer@Serene/lxsameer) lxsameer |
| 2025-02-26 10:36:04 +0100 | <tomsmeding> | what do you mean with "\E f(x)"? |
| 2025-02-26 10:35:35 +0100 | <cheater> | what do you call a pair of functions in mathematics f, g, f: X -> Y and g: Y -> X such that \A x \in X \E f(x) and \A y \in Y \E g(y)? |