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2024-09-25 03:32:01 +0200 | geekosaur | wonders where overshoes fit here 😛 |
2024-09-25 03:31:55 +0200 | <haskellbridge> | <Bowuigi> You could use two shirts as an example instead |
2024-09-25 03:31:50 +0200 | <EvanR> | left leg and right leg |
2024-09-25 03:31:43 +0200 | <EvanR> | two pants |
2024-09-25 03:31:32 +0200 | <monochrom> | mom used to advise "it's winter, put on two pants". (I declined.) |
2024-09-25 03:31:22 +0200 | <EvanR> | not even people who wear sandals and socks do that |
2024-09-25 03:31:02 +0200 | <monochrom> | I think some people do that. |
2024-09-25 03:30:47 +0200 | <monochrom> | OK fine! :) |
2024-09-25 03:30:42 +0200 | <EvanR> | lol |
2024-09-25 03:30:40 +0200 | <monochrom> | :( |
2024-09-25 03:30:33 +0200 | <haskellbridge> | <Bowuigi> Unless you are used to putting socks on top of your shoes |
2024-09-25 03:30:11 +0200 | <haskellbridge> | <Bowuigi> The socks example was an example of a groupoid rather than a group |
2024-09-25 03:29:46 +0200 | <EvanR> | \o/ |
2024-09-25 03:29:33 +0200 | <haskellbridge> | <Bowuigi> It does tho |
2024-09-25 03:28:37 +0200 | <EvanR> | shouldn't the same theorem apply to groupoids |
2024-09-25 03:28:36 +0200 | <monochrom> | Right, without commutativity, the undo of "put on socks, put on shoes" is not "take off socks, take off shoes". |
2024-09-25 03:28:23 +0200 | <EvanR> | a group is like a groupoid where all the objects are the same |
2024-09-25 03:28:21 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) |
2024-09-25 03:28:00 +0200 | <EvanR> | I know how it's too specific |
2024-09-25 03:27:53 +0200 | <EvanR> | waaaaaaaaait |
2024-09-25 03:27:49 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) (Remote host closed the connection) |
2024-09-25 03:26:42 +0200 | <EvanR> | that formula makes way more sense now, ignoring the mathematical proof of it, after thinking of it like invertible functions. If you want to invert "do b, then do a to the product of that", you have to first undo a then undo b |
2024-09-25 03:23:00 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) (Ping timeout: 252 seconds) |
2024-09-25 03:22:04 +0200 | xff0x | (~xff0x@fsb6a9491c.tkyc517.ap.nuro.jp) |
2024-09-25 03:20:12 +0200 | <EvanR> | that's cool |
2024-09-25 03:19:08 +0200 | <Lears> | Ah, no; with identity that's not even a weakening: a * (b * c) = (1 * a) * (b * c) = 1 * ((a * b) * c) = (a * b) * c |
2024-09-25 03:18:10 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) merijn |
2024-09-25 03:17:05 +0200 | <monochrom> | You have used identity, inverse, associativity. So I say yes, you pretty much need a group. |
2024-09-25 03:16:39 +0200 | <Lears> | Groups are pretty general; they only have a few laws. You're already using identity, invertibility and associativity---that's all of them. I suppose you could weaken associativity to `(w * x) * (y * z) = w * ((x * y) * z)`, but I doubt that gives you anything of interest. |
2024-09-25 03:11:49 +0200 | <EvanR> | i.e. is group laws too specific |
2024-09-25 03:11:36 +0200 | <EvanR> | this is a theorem about groups, but does it only work for groups? |
2024-09-25 03:11:17 +0200 | <EvanR> | QED |
2024-09-25 03:11:14 +0200 | <EvanR> | (ab)⁻¹ = b⁻¹a⁻¹ |
2024-09-25 03:11:11 +0200 | <EvanR> | 1 = abb⁻¹a⁻¹ (obviously) |
2024-09-25 03:07:47 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) |
2024-09-25 03:07:30 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) (Ping timeout: 248 seconds) |
2024-09-25 03:07:15 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) (Remote host closed the connection) |
2024-09-25 03:02:24 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) merijn |
2024-09-25 03:01:42 +0200 | peterbecich | (~Thunderbi@syn-047-229-123-186.res.spectrum.com) (Ping timeout: 246 seconds) |
2024-09-25 03:00:55 +0200 | FinnElija | (~finn_elij@user/finn-elija/x-0085643) finn_elija |
2024-09-25 03:00:33 +0200 | FinnElija | (~finn_elij@user/finn-elija/x-0085643) (Remote host closed the connection) |
2024-09-25 02:52:15 +0200 | machinedgod | (~machinedg@d50-99-47-73.abhsia.telus.net) (Ping timeout: 246 seconds) |
2024-09-25 02:51:28 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) (Ping timeout: 252 seconds) |
2024-09-25 02:49:46 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) |
2024-09-25 02:46:36 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) merijn |
2024-09-25 02:35:33 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) (Ping timeout: 248 seconds) |
2024-09-25 02:30:48 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) merijn |
2024-09-25 02:29:28 +0200 | synchromesh | (~john@2406:5a00:241a:5600:b8f8:7fb4:fdd7:b64d) synchromesh |
2024-09-25 02:28:48 +0200 | xff0x_ | (~xff0x@2405:6580:b080:900:3e09:7111:c63e:2d47) (Ping timeout: 246 seconds) |
2024-09-25 02:28:08 +0200 | athan | (~athan@syn-098-153-145-140.biz.spectrum.com) (Quit: Konversation terminated!) |