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When my professor first gave us this problem, I raised a big stink in class and insisted that there were an infinite number of marbles in each bag.
Apparently I am wrong, and I don't completely understand why. Intuitively it makes sense that if you are putting more marbles into a bag than you are removing, then you will always have marbles in the bag, but mathematicaly this doesn't work.
I think the problem has to do with the difference between 'on the way to infinity' and 'at infinity'
If you stop at any finite time, there will be a lot of marbles in the bag, and as time increases, the number of marbles in the bag will increase. However, at time equals infinity, all the marbles in the bag (in problem 1) will have been removed, so the total number of marbles will be 0.
Even though we can find the answer to problems like this one mathematically, I don't think they will ever completely make sense.
this problem was supposed to be a nice introduciton to the wierdness that is cantor sets, and they are even worse.
Oh, and good job CSflim, I didn't want to congratulate you before a discussion got underway.
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"Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill
"All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence
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