Infinite processes riddle A train with infinitely many seats, one for each rational number, stops in countably many villages, one for each positive integer, in increasing order, and then finally arrives at the city.
At the first village, two women board the train. 
At the second village, one woman leaves the train to go visit her cousin, and two other women board the train. 
At the third village, one woman leaves the train to go visit her cousin, and two other women board the train. 
At the fourth village, and in fact at every later village, the same thing keeps happening: one woman off to visit her cousin, two new women on board the train. How many women arrive at the city?

The problem is not well posed, since you don't specify which woman leaves the train at each station. See Ross–Littlewood paradox.
