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2021-03-15 16:58:45 <fresheyeball> is [] = (+ Infinity)?
2021-03-15 16:58:52 → zebrag joins (~inkbottle@aaubervilliers-654-1-101-29.w86-212.abo.wanadoo.fr)
2021-03-15 16:58:54 <__minoru__shirae> geekosaur: yeah, was wondering about that too
2021-03-15 16:59:50 <geekosaur> fresheyeball: look at it in terms of its definition, data List a = [] | Cons a (List a)
2021-03-15 17:00:25 <geekosaur> so not quite (+ Inf), since it can be finite
2021-03-15 17:01:23 <monochrom> Infinite series. [a] = 1 + a + a*a + a*a*a + ...
2021-03-15 17:01:27 <fresheyeball> geekosaur: doesn't that just make it a larger infinite?
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2021-03-15 17:01:55 <codygman`> merijn: Perhaps I'll carry on your "fix bracket" torch from 7 years ago if I ever get this fixed.
2021-03-15 17:01:55 <fresheyeball> If it can be infinite list, or a finite list, doesn't that just mean the cardinality is bigger than a countable infinity?
2021-03-15 17:01:56 <codygman`>
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2021-03-15 17:02:25 <geekosaur> it's still countable
2021-03-15 17:02:36 <monochrom> You are really better off writing out "Maybe a = 1+a" instead of trying to be pointfree with "Maybe = (1 +)". The pointfree form doesn't scale.
2021-03-15 17:03:14 <dminuoso> monochrom: I disagree. Everybody should @pl their code to lambdabot before committing. It scales!
2021-03-15 17:03:28 <dminuoso> Completely pointless code. Guaranteed.
2021-03-15 17:04:01 <fresheyeball> geekosaur: how so? Does the diagonal proof not apply here? Can't I just invent a new list with a different member?
2021-03-15 17:04:36 <geekosaur> it wouldn't describe the same type
2021-03-15 17:04:48 <fresheyeball> [Int] ?
2021-03-15 17:05:00 <fresheyeball> why not?
2021-03-15 17:05:17 <fresheyeball> I don't see why the diagonal proof doesn't apply to lists
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2021-03-15 17:05:48 <geekosaur> maybe I'm misunderstanding you. but if you added an arbitrary thing it would not then be a list of a, but a list of a plus an item of some b /= a
2021-03-15 17:06:03 <fresheyeball> oic
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2021-03-15 17:06:21 <fresheyeball> well I then I think perhaps let's consider this
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2021-03-15 17:06:23 <fresheyeball> [()]
2021-03-15 17:06:32 <fresheyeball> because then no diagonal right?
2021-03-15 17:06:40 <fresheyeball> but still, I can have an infinite list of [()]
2021-03-15 17:06:47 <fresheyeball> and a finite list of arbitrary size
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2021-03-15 17:07:28 <monochrom> That is still not "1 + infinity".
2021-03-15 17:07:59 <monochrom> If [Int] were = 1 + infinity, where is "Int" in "1 + infinity"?
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2021-03-15 17:08:10 <monochrom> err sorry misread, nevermind.
2021-03-15 17:08:26 <fresheyeball> I start counting like this
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2021-03-15 17:08:29 <fresheyeball> [] = 1
2021-03-15 17:08:33 <fresheyeball> [()] = 2
2021-03-15 17:08:34 <monochrom> But [()] is still not () + infinity. [Int] is still not Int + Infinity. (Where is the empty list?)
2021-03-15 17:08:38 <fresheyeball> [(), ()] = 3
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2021-03-15 17:09:08 <monochrom> How about [Int]? How abou [Bool]?
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2021-03-15 17:09:29 <monochrom> Where is [True, False, False, True, False] in your scheme?
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2021-03-15 17:09:53 <fresheyeball> Well if [()] is an uncountable infinity, because of infinite lists in addition to an infinite number of finite lists.
2021-03-15 17:10:00 → RusAlex_ joins (~Chel@BSN-77-82-41.static.siol.net)
2021-03-15 17:10:02 <fresheyeball> then I think it doesn't matter actually
2021-03-15 17:10:17 <fresheyeball> Whatever we put in the list, it wont change the cardinality
2021-03-15 17:10:22 <hyperisco> fresheyeball, the arithmetic interpretation is just the same as if you have a recursive arithmetic expression
2021-03-15 17:10:39 <hyperisco> fresheyeball, so you can analyse in various ways... it is an infinite series
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2021-03-15 17:12:05 <hyperisco> fresheyeball, for example you can rearrange to a polynomial and, interestingly, the derivative is the same as the zipper https://pavpanchekha.com/blog/zippers/derivative.html
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2021-03-15 17:12:57 <fresheyeball> math buddy of mine in another channel is telling me it's aleph nought
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2021-03-15 17:13:13 <geekosaur> there''s some questions there iirc
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2021-03-15 17:14:00 <geekosaur> well, no, aleph0 is pretty well accepted, it's the next one up there are questions about. but they're just describing countable infinity in another way
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