Newest at the top
| 2024-09-25 03:38:50 +0200 | Smiles | (uid551636@id-551636.lymington.irccloud.com) (Quit: Connection closed for inactivity) |
| 2024-09-25 03:38:45 +0200 | <EvanR> | microwaves, nanowaves, picowaves |
| 2024-09-25 03:37:46 +0200 | <geekosaur> | err, prefixes |
| 2024-09-25 03:37:41 +0200 | <geekosaur> | then they just gave up and switched to Greek suffixes |
| 2024-09-25 03:37:09 +0200 | <geekosaur> | that made perfect sense until they figured out how to generate and control microwave frequencies |
| 2024-09-25 03:36:16 +0200 | <monochrom> | Err, s/HS/HF/ # VHF, UHF |
| 2024-09-25 03:35:49 +0200 | ystael | (~ystael@user/ystael) (Ping timeout: 248 seconds) |
| 2024-09-25 03:35:32 +0200 | <monochrom> | haha |
| 2024-09-25 03:34:54 +0200 | <geekosaur> | overshoe_{\omega} |
| 2024-09-25 03:34:27 +0200 | <EvanR> | that's why the layers are indexed by an ordinal |
| 2024-09-25 03:34:05 +0200 | <monochrom> | I mean, if you start having two layers of overshoes, the outer layer would have to be called something like "ultrashoes" or something ridiculous and soon you will run out of superlatives. |
| 2024-09-25 03:34:05 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) (Remote host closed the connection) |
| 2024-09-25 03:33:57 +0200 | <EvanR> | highspeed CMOS |
| 2024-09-25 03:33:57 +0200 | merijn | (~merijn@204-220-045-062.dynamic.caiway.nl) merijn |
| 2024-09-25 03:33:09 +0200 | <monochrom> | The "VHS, UHS, HD, UHD, VVVVUUUUHD" progression applies. |
| 2024-09-25 03:32:37 +0200 | <monochrom> | I don't suppose you would put on two layers of overshoes? |
| 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) |