Ross-Littlewood vase filling paradox (from Wikipedia): To complete an infinite number of steps, it is assumed that the vase is empty at one minute before noon, and that the following steps are performed: The first step is performed at 30 seconds before noon. The second step is performed at 15 seconds before noon. Each subsequent step is performed in half the time of the previous step, i.e., step n is performed at 2−n minutes before noon. This guarantees that a countably infinite number of steps is performed by noon. Since each subsequent step takes half as much time as the previous step, an infinite number of steps is performed by the time one minute has passed. At each step, ten balls are added to the vase, and one ball is removed from the vase. The question is then: How many balls are in the vase at noon? To me, it is somewhat obvious that it is ω+ω+ω+ω+ω+ω+ω+ω+ω. (9ω's). Where am I wrong/what am I missing?