In terms of the question, “Are there more infinite sequences that contain Hamlet or more that don’t?”- in the context of true randomness and truly infinite sequence, this feels like almost a trick question. Almost every truly random infinite sequence will contain Hamlet an infinite number of times, along with every other possible finite sequence (e.g., Moby Dick, War and Peace, you name it). In fact, the probability of a random infinite sequence not containing Hamlet is effectively zero.
Where it becomes truly interesting is if you have an infinite number of infinite sequences. Now you’d certainly get instances of those “effectively zero” cases, but only in ratios within infinity itself, haha. I guess that’s probably what you were getting at?
Fair enough, I suppose it is interesting!
In terms of the question, “Are there more infinite sequences that contain Hamlet or more that don’t?”- in the context of true randomness and truly infinite sequence, this feels like almost a trick question. Almost every truly random infinite sequence will contain Hamlet an infinite number of times, along with every other possible finite sequence (e.g., Moby Dick, War and Peace, you name it). In fact, the probability of a random infinite sequence not containing Hamlet is effectively zero.
Where it becomes truly interesting is if you have an infinite number of infinite sequences. Now you’d certainly get instances of those “effectively zero” cases, but only in ratios within infinity itself, haha. I guess that’s probably what you were getting at?