You have an empty container, and an infinite number of marbles, each numbered with an integer from 1 to infinity.
At the start of the minute, you put marbles 1 - 10 into the container, then remove one of the marbles and throw it away. You do this again after 30 seconds, then again in 15 seconds, and again in 7.5 seconds. You continuosly repeat this process, each time after half as long an interval as the time before, until the minute is over.
Since this means that you repeated the process an infinite number of times, you have "processed" all your marbles.
How many marbles are in the container at the end of the minute if for every repetition (numbered N)
A. You remove the marble
numbered (10 * N)
B. You remove the marble numbered (N)
(In reply to
re: Interestingly by DJ)
Excuse me, but no.
Both the number inside and outside are of the same cardinality. Just because the particular map you chose from one set to the other is not onto, does not mean there is no such map. Every integer is a rational number, but not conversely. However, it is well known (and not hard to show) that there are exactly as many rational numbers as integers.
As Eric posted, trying to deal with orders of infinity in "real world" situations can lead to seemingly silly results. This is of course why this problem is in the "Paradoxes" category.
I find it particularly interesting that in both (A) and (B) there are 9 times as many marbles in the container as have been discarded AT EACH STEP OF THE PROCESS. But the end results are quite different....
re(2): Interestingly
