magz :3

i think for my purposes i’m fine with hosting that through a separate service, so instead of XMPP + mumble i would run polyproto + mumble (or some other voip solution, screen sharing seems to be a decent way away in mumble)

but (as i understand it), polyproto isn’t a chat protocol per se, but more a protocol for federated message authentication. as an application of this protocol, they’re building polyproto-chat, which is a chat protocol. in theory, one could then also build a polyproto-voice so you can use the same account for both chatting and voice calls. i still think this is pretty far away, considering how young polyproto is, which is why my current vision is chat and voice as two separate services (which i also prefer because i imagine it makes the technology simpler and hosting easier)

i honestly think that if revolt had federation, then it would be the obvious choice for me, but alas. personally i’m still hopeful for polyproto getting off the ground, but the boring realistic choice for the time being is probably something like XMPP + mumble

actually you can show that the naturals, integers and rationals all have the the same size.
for example, to show that there are as many naturals as integers (which you do by making a 1-to-1 mapping (more specifically a bijection, i.e. every natural maps to a unique integer and every integer maps to a unique natural) between them), you can say that every natural, n, maps to (n+1)/2 if it is odd and -n/2 if it is even. so 0 and 1 map to themselves, 2 maps to -1, 3 maps to 2, 4 maps to -2, and so on. this maps every natural number to an integer, and vice-versa. therefore, the cardinality (size) of the naturals and the integers are the same.

you can do something similar for the rationals (if you want to try your hand at proving this yourself, it can be made a lot easier by noting that if you can find a function that maps every natural to a unique rational (an injection), and another function that maps every rational to a unique natural, you can use those construct a bijection between the naturals and rationals. this is called the schröder-bernstein theorem).

it turns out that you cannot do this kind of mapping between the naturals (or any other set of that cardinality) and the reals. i won’t recite it here, but cantor’s diagonal argument is a quite elegant proof of this fact.

now, this raises a question: is there anything between the naturals (and friends) and the reals? it turns out that we don’t actually know. this is called the continuum hypothesis

i think the argument here is more that saying “you can use this however you like, no questions asked” is a bad idea because it allows corporations to approriate the work

if you have a pipeline running eslint on all your PRs (which you should have!), you can set no-explicit-any as an error in your eslint config so it’s impossible to merge code with any in it