Except that in the original problem, there cannot be more days than people;
...each day, one more person gets permanently transferred across to... (Emphasis added.)
Then again, rephrasing the problem in equivalent ways has interesting effects:
Assume that the number of people is countable; assign each of them a natural number, but don’t tell them which one it is.
Suppose that on the Nth day you move the person with the Nth prime number to the opposite sphere; every individual prefers case 1, where they have 100% chance of infinite happiness.
Suppose that you tell everyone their number and on the Nth day you move the person with the Nth number to the opposite sphere; every individual prefers case 2, where they have a finite period of agony followed by infinite happiness.
What’s the Erdos number of an infinite number of monkeys juggling an infinite number of bananas?
Except that in the original problem, there cannot be more days than people;
Then again, rephrasing the problem in equivalent ways has interesting effects:
Assume that the number of people is countable; assign each of them a natural number, but don’t tell them which one it is.
Suppose that on the Nth day you move the person with the Nth prime number to the opposite sphere; every individual prefers case 1, where they have 100% chance of infinite happiness.
Suppose that you tell everyone their number and on the Nth day you move the person with the Nth number to the opposite sphere; every individual prefers case 2, where they have a finite period of agony followed by infinite happiness.
What’s the Erdos number of an infinite number of monkeys juggling an infinite number of bananas?