I thought that at first... But then for every infinite series with exactly one hamlet in it, there's an infinite series where one character is wrong. And there's another one where a different character is wrong... And so on and so on. Even if the series contains an infinite number of hamlets, you can replace one character in each in a huge number of ways! It starts to seem like there are more options with almost Hamlet than there are specifically with Hamlet.

In fact, I begin to wonder if almost any constraint reducing the search space in the infinite set of such infinite sequences, you will inevitably have fewer items within the search space than without... Since you can usually construct multiple non-matching candidates from any matching one.

But... Honestly I'm not sure how much any of that matters in infinite contexts. Since they are impossible it boggles my mind trying to imagine it.