Yes, sorry, there is definitely a theorem that if you have an infinite sequence, uniformly distributed over an alphabet, then the probability of seeing any fini

Yes, sorry, there is definitely a theorem that if you have an infinite sequence, uniformly distributed over an alphabet, then the probability of seeing any finite sequence is 1. I think that, given some assumptions, you can model the universe as an infinite numerical sequence, so you should see all finite events. However, the assumptions here seem tricky. Uniform distribution of probability seems unlikely, and if the universe is anything like the game of life, there are garden of Eden states with no predecessor state, which an evolving system cannot reach, even in infinite time. Cardinality is indeed tricky. I had thought that all finite sequences would be greater than aleph-null, but apparently it isn't.