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 both cases, you put in ten marbles then discard one, which means that 9/10 of the marbles are in the container at the end of any of any given cycle, and 1/10 of the marbles have been discarded. Which means after having completed this process an infinte number of times, you would have 9/10 infinity marbles in the container, and 9/10 of infinity is still infinity.

In other words although you would have taken a infinite number of marbles away, you would still have 9 times as many marbles in the container, so the container would also contain an infinite number of marbles. Remember that infinity can be divided by any finite number and still equal infinity.

By the way in order to disprove that the container would contain an infinite number of marbles, you would also need to disprove some or all of the theoroms that calculus is based on.

Posted by Jon on 2004-09-10 05:01:52