alt Hacker News"almost surely" means "happens with a probability 1", which in infinite set contexts doesn't mean that there aren't other outcomes, but that they have probability 0.
So like, imagine that you had some finite list of integers, and you were picking a random number from 0 to infinity - because the domain is infinite, any finite set has 0 probability, but that doesn't mean it doesn't exist.
Thank you. That makes this a pretty big deal doesn't it?
The ability to deterministcly identify that code eventually reaches a halting state, implies that we can use these stochastic tools to generate deterministic outcomes reliably in the future doesn't it?