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)
With scenario A, after n iterations, the marbles you've taken out of the jar are:
{ 10, 20, 30, ... n * 10 }
The marbles still left in the jar are:
{ 1, 2, 3 ... n * 10 } - { 10, 20, 30 ... n * 10 }
With scenario B, after n iterations, the marbles you've taken out of the jar are:
{ 1, 2, 3, ... n }
And the marbles that are still left in the jar are:
{ n + 1, n + 2, n + 3, ... n * 10 }
The latter set is clearly larger than the former, by a factor of nine. It continues to be larger, even as n approaches infinity. This confirms what common sense is (or, at least, should be) telling you: You're adding nine marbles to the jar with every iteration.
Don't trick yourself into thinking that "infinity" is a number. One doesn't do "infinity" iterations the way one does "seven" iterations, and infinity minus infinity does not (always) equal zero.
rock on
dave
The marbles that are still in the jar...
