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2020-09-27 05:37:39 <solonarv> the ordinals are ordered (obviously), so this gives you a notion of size that is more fine-grained than cardinality
2020-09-27 05:37:40 <nshepperd> is that like defining 'same size' = 'there exists a order preserving bijection'?
2020-09-27 05:37:48 <solonarv> hm, yes, I think so
2020-09-27 05:38:27 × mu__ quits (~mu@unaffiliated/mu) (Read error: Connection reset by peer)
2020-09-27 05:38:48 → mu_ joins (~mu@unaffiliated/mu)
2020-09-27 05:39:17 <nshepperd> interesting
2020-09-27 05:39:43 <solonarv> this is "finer-grained" in that if two ordered sets are the same size by this definition, then they are also the same size if you forget the ordering and look for any bijection
2020-09-27 05:41:17 <nshepperd> so like the rational numbers are bigger than the natural numbers in that sense, because any two rational numbers has one between them
2020-09-27 05:41:37 <nshepperd> the rational numebrs with the standard ordering that is
2020-09-27 05:41:46 <dolio> The usual ordering on the rationals isn't a well-order.
2020-09-27 05:42:17 → snakemasterflex joins (~snakemast@213.100.206.23)
2020-09-27 05:42:30 <nshepperd> does it have to be a well order
2020-09-27 05:42:42 <dolio> If you want it to be an ordinal.
2020-09-27 05:44:03 <dolio> I mean, I don't think the ordinal ordering is usually considered to be "size" either. That is reserved for cardinality.
2020-09-27 05:46:58 hackage unboxing-vector 0.2.0.0 - A newtype-friendly variant of unboxed vectors https://hackage.haskell.org/package/unboxing-vector-0.2.0.0 (aratamizuki)
2020-09-27 05:48:32 × mu_ quits (~mu@unaffiliated/mu) (Read error: Connection reset by peer)
2020-09-27 05:48:49 → mu_ joins (~mu@unaffiliated/mu)
2020-09-27 05:49:18 <dolio> Anyhow, using the naturals or the rationals doesn't really change the ordinals you can can define, which is the point of cardinality, I guess.
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2020-09-27 05:49:47 <dolio> You can put the same well-orders on either one.
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2020-09-27 06:00:02 × fimp quits (~fimp@193.56.252.210) ()
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2020-09-27 06:00:44 <nshepperd> https://en.wikipedia.org/wiki/Order_type seems to be the thing
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