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| 2026-01-16 00:31:21 +0100 | <monochrom> | 2-colourability is polynomial-time, 3-colourability is NP-complete. |
| 2026-01-16 00:31:10 +0100 | <int-e> | bitstream adds additional observations for each natural number. |
| 2026-01-16 00:30:54 +0100 | <monochrom> | SillyType is countable, BitStream is uncountable. |
| 2026-01-16 00:30:51 +0100 | <int-e> | jreicher: NO! |
| 2026-01-16 00:30:35 +0100 | <jreicher> | monochrom: hang on, are you now saying bitstream is countable? I was hoping that, having proved SillyType is countable, you'd now prove bitstream is uncountable. |
| 2026-01-16 00:30:22 +0100 | <monochrom> | Generally there are multiple instance when switching from 1 to 2, or 2 to 3, or 3 to 4 makes breaking changes. |
| 2026-01-16 00:30:04 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn |
| 2026-01-16 00:29:56 +0100 | __monty__ | (~toonn@user/toonn) (Quit: leaving) |
| 2026-01-16 00:29:51 +0100 | k0zy | (~user@user/k0zy) k0zy |
| 2026-01-16 00:29:51 +0100 | k0zy | (~user@75-164-179-179.ptld.qwest.net) (Changing host) |
| 2026-01-16 00:29:43 +0100 | k0zy | (~user@75-164-179-179.ptld.qwest.net) |
| 2026-01-16 00:29:37 +0100 | <int-e> | Sure. It's morally finite ("morally" being the view where you don't have bottoms) |
| 2026-01-16 00:29:36 +0100 | <monochrom> | But intuitively I'm not surprised. Expressing natural numbers in unary requires n units of memory for n; "merely" switching to binary, that drops down to lg n. |
| 2026-01-16 00:28:51 +0100 | <jreicher> | And so SillyType is countable, yes? |
| 2026-01-16 00:27:29 +0100 | <monochrom> | I map 0 to the infinite stream z = I z, 1 to bottom, 2 to I bottom, 3 to I (I bottom), etc. |
| 2026-01-16 00:26:51 +0100 | <jreicher> | Every proof I sketch out results in an inconsistency. |
| 2026-01-16 00:26:25 +0100 | <jreicher> | No, prove away, please. I'd like to understand. |
| 2026-01-16 00:26:11 +0100 | <monochrom> | I can prove them, but if you're asking for intuition, I think I don't have any. |
| 2026-01-16 00:25:59 +0100 | <jreicher> | Surely they're either both countable, or both uncountable, depending on your "definitions" |
| 2026-01-16 00:25:35 +0100 | <jreicher> | I still don't understand why anyone would say SillyType is countable but BitStream is uncountable. |
| 2026-01-16 00:20:22 +0100 | <EvanR> | imaginary numbers are real and real numbers are fictional |
| 2026-01-16 00:20:08 +0100 | <monochrom> | My beef is that "imaginary number" is a misnomer. But I digress. |
| 2026-01-16 00:20:04 +0100 | <jreicher> | Fictionalists unite |
| 2026-01-16 00:19:48 +0100 | <EvanR> | lol |
| 2026-01-16 00:19:43 +0100 | <int-e> | EvanR: "real number" is a misnomer :P |
| 2026-01-16 00:19:40 +0100 | <EvanR> | I'm doing vibes there |
| 2026-01-16 00:19:29 +0100 | <jreicher> | I'm really not doing vibes, so I don't know why you keep saying that |
| 2026-01-16 00:19:26 +0100 | <EvanR> | at least approximately |
| 2026-01-16 00:19:21 +0100 | <EvanR> | well you know where infinitesimals are |
| 2026-01-16 00:19:08 +0100 | <EvanR> | if were doing vibes, this kind of defeats the point of the real line, and the idea of quantity or ordering |
| 2026-01-16 00:19:05 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) (Ping timeout: 245 seconds) |
| 2026-01-16 00:19:04 +0100 | <jreicher> | I'm pretty sure non-standard analysis does this with asserting the existence of infinitisimals |
| 2026-01-16 00:18:19 +0100 | <jreicher> | yes of course. :) |
| 2026-01-16 00:18:11 +0100 | <EvanR> | at least approximately |
| 2026-01-16 00:17:49 +0100 | <EvanR> | but it would seem kind of odd that these objects don't "sit" somewhere on the real line xD |
| 2026-01-16 00:17:34 +0100 | <EvanR> | I don't doubt you can throw exotic objects in |
| 2026-01-16 00:15:49 +0100 | <jreicher> | I never have |
| 2026-01-16 00:15:43 +0100 | <dolio> | So you can't assume that real numbers are the same things as expansions. |
| 2026-01-16 00:15:43 +0100 | Googulator | (~Googulato@2a01-036d-0106-29ac-fd48-b0ea-63d3-602a.pool6.digikabel.hu) (Quit: Client closed) |
| 2026-01-16 00:15:39 +0100 | Googulator69 | (~Googulato@2a01-036d-0106-29ac-fd48-b0ea-63d3-602a.pool6.digikabel.hu) |
| 2026-01-16 00:15:12 +0100 | <jreicher> | I'm not confused about that. Every bitstream can be interpreted as a numeral corresponding to a number. But that says nothing about the converse, especially since nothing stops you from throwing in all kinds of exotic objects to the set you want to call "the reals" |
| 2026-01-16 00:15:08 +0100 | <dolio> | Yeah, like I said, there's a paper about a topos where the reals are countable. But the diagonal argument holds in every topos. |
| 2026-01-16 00:14:38 +0100 | <EvanR> | if you didn't guess already the argument in the paper is answering "no" to its title... like betteridge's law |
| 2026-01-16 00:14:36 +0100 | trickard_ | (~trickard@cpe-84-98-47-163.wireline.com.au) |
| 2026-01-16 00:14:22 +0100 | trickard_ | (~trickard@cpe-84-98-47-163.wireline.com.au) (Read error: Connection reset by peer) |
| 2026-01-16 00:14:20 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn |
| 2026-01-16 00:13:49 +0100 | <EvanR> | if you keep getting confused thinking stream of bits means "oh reals", and reals means "oh, just a binary expansion", then that equivocation is the point of this old paper |
| 2026-01-16 00:12:35 +0100 | <EvanR> | that's specifically about reals |
| 2026-01-16 00:12:26 +0100 | <EvanR> | that was being discussed |
| 2026-01-16 00:12:19 +0100 | <EvanR> | you brought up chaitin |