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)
Thank you for finally getting of your track. What I've really been trying to do is show you that the math is irrelevant here - it is the interpretation of the problem itself from where the paradox is derived (note the problem is in the category "paradoxes", not "math"). The problem, boiled down, becomes simply a mathematical way of asking the same question as is asked in "the guilty demon". You have chosen to ignore the implications of such. I have chosen (by re-working the problem) to ignore different constraints. These different sets of assumptions are in fact both faulty. It is the problem itself that is faulty, and in fact there is no answer to this question.
PS, I don't agree that I can't create an infinite sum by infinitly adding a constant term. This is a basic tenet of calculus.
Also on a side note, and I'll happily reiterate that I have no experience in set theory, so this might be a silly question (and its just out of curiousity, not as any form of attack on your math etc.), you mentioned that this aleph null is defined as the smallest infinity - what heppens to this if you take away one? Is this simply another definition that must be taken for granted or is there some reasoning involved?
It's been interesting.
finally
