TIL it’s an open problem whether there exists a polynomial bijection from Q to QxQ and therefore apparently a very very difficult question.

who knew?

I haven’t used but reading the comments it seems a bit clunky if viewed solely from that perspective. I think with enough volume you could justify a market maker that can actually quote prices and redeem instantly.

I once wasted an entire hour of pitching Axiom listening to some public pension plan schlub tell me how farcaster is the future and that it’s very existence proves crypto is a better stack to build apps on that route around bitcoin entirely. I hope the plan’s beneficiaries thank him for his service.
@nevent1qqs...

with enough volume you could turn this into a fully fledged p2p exchange.

speaking of which, @nprofile1q..., do you even believe the reals exist?

doesn’t it feel weird? Q has infinitely many holes in it.

heine borel and anything relying on compactness fails.

weirdest/coolest result is IVT fails too, which is bizarre because on R continuity is strictly stronger than IVP, but in dense-but-not-complete R that flips.

they don’t tell you that virtually every concept surrounding continuity works on functions from Q to Q.

they don’t tell you this because they want you to be ignorant and afraid.

so interesting:

https://www.youtube.com/watch?v=jxu80s5vvzk

ah but you are assuming the algebra works such that (a,b)*(c,d)=(a*c,b*d) whereas I am analogising it to how C works with reals.

😂

think of it this way: to perform any arithmetic operation in QxQ you can only possibly require multiplication and addition of rationals, which, given Q is closed (just not complete) will give you answers in QxQ too.