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)

It seems to argue about infinity purely depends on point of view. Human nature can not completly accept it in our terms because we use numbers to describe the essence of 'how many' in counting. If I have balls number 1 - infinity, and friend a has balls all odd to infinity and friend b all even, then by our thinking, I have twice as many as both of them. But they can each claim to match a ball to mine. If I remove all odds from my stack, I have an all even stack.
But:

∞ - ∞ = ∞

Which if you follow means ∞ = 0 in our mathematical scale.
Basically, don't bring it into normal algebraic maths, COS IT WONT WORK.

Posted by Dacre on 2003-09-22 10:27:51