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 circles by Cory Taylor)

Saying that you’re labeling marbles one to infinity (which would then include infinity, as marbles 1 to 5 include the marble 5) defies the definition of the term infinity.

You cannot simultaneously say hat you've processed all the marbles and that there are still marbles being processed. If you finish, there is a last. If there is a last, there was never an infinity.

There are an infinite number of numbers greater than infinity.

Two sets with infinite size do not necessarily have the same size.

:)

Posted by Cory Taylor on 2003-09-16 18:47:01