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| 2025-11-21 12:04:10 +0100 | <lucabtz> | chromoblob yep |
| 2025-11-21 12:04:04 +0100 | califax | (~califax@user/califx) (Ping timeout: 272 seconds) |
| 2025-11-21 12:03:41 +0100 | EvanR | (~EvanR@user/evanr) (Ping timeout: 264 seconds) |
| 2025-11-21 12:03:34 +0100 | <yin> | does the Yoneda Lemma apply? |
| 2025-11-21 12:03:30 +0100 | <lucabtz> | but does not exclude {} in the example A = B = {} |
| 2025-11-21 12:03:28 +0100 | <chromoblob> | yeah, i wanted to lead to this |
| 2025-11-21 12:03:14 +0100 | <lucabtz> | which does exclude {} from the example of A = B = {1} |
| 2025-11-21 12:03:03 +0100 | mesaoptimizer | (~user@user/PapuaHardyNet) PapuaHardyNet |
| 2025-11-21 12:03:02 +0100 | <c_wraith> | lucabtz: in set theory, yes. In domain theory? |
| 2025-11-21 12:02:52 +0100 | <lambdabot> | Void -> Void |
| 2025-11-21 12:02:51 +0100 | <[exa]> | :t id :: Void -> Void |
| 2025-11-21 12:02:48 +0100 | <lucabtz> | chromoblob i think in general a subset of A x B is called a relation between A and B. for a function the relation has to assign a single element of B to each and every element of A |
| 2025-11-21 12:02:44 +0100 | fp | (~Thunderbi@2001:708:20:1406::1370) fp |
| 2025-11-21 12:02:36 +0100 | <haskellbridge> | <Morj> chromoblob: How extentional of you |
| 2025-11-21 12:02:01 +0100 | <c_wraith> | because there are multiple concepts of function, and a lot of the disagreement is coming from set theory vs domain theory |
| 2025-11-21 12:01:54 +0100 | <chromoblob> | Morj: one, because any two are indistinguishable |
| 2025-11-21 12:01:32 +0100 | <c_wraith> | here's where things get annoying: you need to be more precise than "function" |
| 2025-11-21 12:01:26 +0100 | <chromoblob> | lucabtz: which restrictions are there on the subset? |
| 2025-11-21 12:01:25 +0100 | <haskellbridge> | <Morj> But how many functions are there from bottom to bottom? One or infinitely many? |
| 2025-11-21 12:01:12 +0100 | EvanR_ | (~EvanR@user/evanr) EvanR |
| 2025-11-21 12:01:01 +0100 | <yin> | and how many functions are there of the type Void -> Void? |
| 2025-11-21 12:00:32 +0100 | <chromoblob> | yin: yes, () would correspond to 1 |
| 2025-11-21 12:00:27 +0100 | <c_wraith> | yes |
| 2025-11-21 12:00:25 +0100 | <lucabtz> | since A x B = {(1, 1)} you have both {} and {(1, 1)} |
| 2025-11-21 12:00:15 +0100 | <yin> | 0^0 would be Void -> Void and not () -> () right? |
| 2025-11-21 12:00:04 +0100 | <lucabtz> | but if {} is a function the you have two functions from A->B |
| 2025-11-21 11:59:49 +0100 | <lucabtz> | because if you take f:A -> B and A = B = {1}, the set of functions from A->B has has cardinality 1 |
| 2025-11-21 11:59:07 +0100 | <lucabtz> | though i think it should be a non-epty subset |
| 2025-11-21 11:59:01 +0100 | kritzefitz | (~kritzefit@debian/kritzefitz) kritzefitz |
| 2025-11-21 11:58:16 +0100 | Frostillicus | (~Frostilli@pool-71-174-119-69.bstnma.fios.verizon.net) (Ping timeout: 264 seconds) |
| 2025-11-21 11:58:04 +0100 | <lucabtz> | yep |
| 2025-11-21 11:57:59 +0100 | <lucabtz> | is correct |
| 2025-11-21 11:57:56 +0100 | <chromoblob> | well, there you have it, {} is the function |
| 2025-11-21 11:57:53 +0100 | <lucabtz> | so maybe 1 |
| 2025-11-21 11:57:49 +0100 | <lucabtz> | well i suppose {} is a subset of {} x {} |
| 2025-11-21 11:57:33 +0100 | kritzefitz | (~kritzefit@debian/kritzefitz) (Remote host closed the connection) |
| 2025-11-21 11:57:25 +0100 | <chromoblob> | hmmmm |
| 2025-11-21 11:57:19 +0100 | <lucabtz> | but {} x {} = {} |
| 2025-11-21 11:57:11 +0100 | <lucabtz> | a function from a set A to B is a subset of A x B with some properties |
| 2025-11-21 11:56:40 +0100 | <chromoblob> | why zero? id is a correct example |
| 2025-11-21 11:56:18 +0100 | <lucabtz> | but by that definition it would be 0 |
| 2025-11-21 11:56:10 +0100 | <lucabtz> | chromoblob shouldnt it be the number of function from an empty set to an empty set? |
| 2025-11-21 11:55:40 +0100 | <[exa]> | <3 |
| 2025-11-21 11:55:17 +0100 | <chromoblob> | 0^0 for me is simply the number of functions from bottom to bottom :) |
| 2025-11-21 11:54:40 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 264 seconds) |
| 2025-11-21 11:54:16 +0100 | <jreicher> | I didn't say 1 wasn't the limit in some situations. I'm just saying it's not the limit in all, so it can't be the definition. |
| 2025-11-21 11:53:34 +0100 | <[exa]> | jreicher: counter-countered by `lim x->0 x^x` and `lim x->0 x^0` |
| 2025-11-21 11:53:04 +0100 | <jreicher> | (counterexample, not a definition) |
| 2025-11-21 11:52:34 +0100 | <jreicher> | lim x->0 0^x |
| 2025-11-21 11:51:25 +0100 | <chromoblob> | yin: 1 |