> FWIW, I think this is the same as saying "iff it is bounded and has finite discontinuities".
It is not: for example, the piece-wise constant function f: [0,1] -> [0,1] which starts at f(0) = 0, stays constant until suddenly f(1/2) = 1, until f(3/4) = 0, until f(7/8) = 1, etc. is Riemann integrable.
"Continuous almost everywhere" means that the set of its discontinuities has Lebesgue measure 0. Many infinite sets have Lebesgue measure 0, including all countable sets.
Until this post it wasn't clear to me that just opening and trusting a directory can cause code to be run without taking any other explicit actions that seem like they might involve running code, like running tests. My bad, but still!
> We never talk about it now because we obviously blew past it years ago.
It's shocking to me that (as far as I know) no one has actually bothered to do a real Turing test with the best and newest LLMs. The Turing test is not whether a casual user can be momentarily confused about whether they are talking to a real person, or if a model can generate real-looking pieces of text. It's about a person seriously trying, for a fair amount of time, to distinguish between a chat they are having with another real person and an AI.
Q: Do you play chess?
A: Yes.
Q: I have K at my K1, and no other pieces. You have only K at K6 and R at R1.
It is your move. What do you play?
A: (After a pause of 15 seconds) R-R8 mate.