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(7): Respectfully, I disagree with all (save perhaps eric)
In a sense I actually agree with what FatBoy is trying to say, though not because of any of this stuff about infinite sets becoming finite sets. Or maybe because of that. He is claiming that, if you could stop, you would have a finite set (likewise, if you could stop the last marble would be either even or odd). What I think he is doing wrong is to say that, since you do stop, you then do have a finite set. I think, rather, that since you cannot end with a finite set (it is absurd, as people have said), you cannot stop.
I think I mentioned Thomson's lamp in some other question. If you turn on a lamp at 30 seconds, turn it off at 45 seconds, on at 52.5 seconds and so on, is the lamp on or off at the end of the time? We can't answer this question. However, it is strictly not a paradox: it's based on a premise which is logically incoherant, that he has to perform an infinite number of descrete tasks in a finite amount of time. Ditton for the marbles. *Not* ditto, however, for any of Zeno's paradoxes, as the tasks are not descrete.
An argument that starts from impossible premises and leads to an apparent paradox is not difficult to create: All brown haired people are six foot tall, all brown eyed people are four foot tall, I am brown haired and brown eyed. How tall am I?
The point was not to bring this off topic (appologies), but to show that saying that premises are logically incoherent is not running away from the question, but can be an equally valid answer.
Posted by Sam
on 2003-09-09 16:29:34