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| 2025-02-26 11:09:54 +0100 | <ames> | just don't listen to nlab when it comes to type theory |
| 2025-02-26 11:09:10 +0100 | <tomsmeding> | I'd personally expect that as soon as that bouncing has any kind of _property_ (it converges, or you end up where you started, ...) then it _does_ have a name |
| 2025-02-26 11:06:18 +0100 | <cheater> | even smoothly so |
| 2025-02-26 11:06:11 +0100 | <cheater> | and can be continuated |
| 2025-02-26 11:05:47 +0100 | <cheater> | and a topology |
| 2025-02-26 11:05:44 +0100 | <cheater> | it can easily create congruences, for example |
| 2025-02-26 11:04:59 +0100 | <cheater> | anyways i think the idea of being able to bounce back and forth an infinite amount of times is pretty interesting |
| 2025-02-26 11:04:44 +0100 | <cheater> | you don't know about ncatlab? |
| 2025-02-26 11:04:00 +0100 | acidsys | (~crameleon@openSUSE/member/crameleon) (Ping timeout: 244 seconds) |
| 2025-02-26 11:02:38 +0100 | <[exa]> | oh that's a nice site. |
| 2025-02-26 11:01:12 +0100 | acidjnk_new | (~acidjnk@p200300d6e7283f8044b147bcd5cee5e7.dip0.t-ipconnect.de) (Ping timeout: 272 seconds) |
| 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? |