Ross–Littlewood paradox

More specifically, like the Thomson's lamp paradox, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which an infinite number of tasks are completed sequentially.

The problem starts with an empty vase and an infinite supply of balls.

Ross's probabilistic version of the problem extended the removal method to the case where whenever a ball is to be withdrawn that ball is uniformly randomly selected from among those present in the vase at that time.

He showed in this case that the probability that any particular ball remained in the vase at noon was 0 and therefore, by using Boole's inequality and taking a countable sum over the balls, that the probability the vase would be empty at noon was 1.

This solution corresponds mathematically to taking the limit inferior of a sequence of sets.

The following procedure outlines exactly how to get a chosen n number of balls remaining in the vase.

This solution is favored by philosopher of mathematics Paul Benacerraf.

This is the solution favored by mathematician and philosopher Jean Paul Van Bendegem.