Another lot of lots of balls

Originally posted by Jirakon
Actually, I wouldn't mind just labelling all the remaining balls with "infinity". It may not be very elegant, but it's better (in my mind) than thinking the set {1, 2, 3,...} of the total number of balls at each step converges to zero 😕

It doesn't converge, there's a discontinuity due to the properties of the cardinality of infinite sets.