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"Case 1 says it might be infinitely many, case two says it might be none." What? Case 2 says that all the balls will be put back in. In both cases, there will

by mankyd 14y ago

"Case 1 says it might be infinitely many, case two says it might be none." What? Case 2 says that all the balls will be put back in. In both cases, there will be infinitely many balls back in the barrel after midnight.

ColinWright 14y ago
Article: "Case 1 says it might be infinitely many, case two says it might be none." > What? Case 2 says that all the balls will be put > back in. In both cases, there will be infinitely > many balls back in the barrel after midnight. Yes, and in case 2 there will be none outside, which is what's being asked. Quoting more completely: How many are outside of the barrel after midnight? We can't tell! Without being explicit, without actually naming the balls and saying which ones are being removed and replaced we simply cannot tell. Case 1 says it might be infinitely many, case two says it might be none. Case two has all the balls in the barrel after midnight. That means there are none outside, which is what's being asked. Or have I misunderstood you?
- mankyd 14y ago
  Ah, my mistake, you are correct. That being said, the example has another flaw: it is based on completing an infinite number of finite time tasks in finite time. That is to say, adding and removing an infinite number of balls will take an infinite amount of time, but we're only given an hour to do it in. Note that this is different from Zeno's paradox, wherein the two racers each have to move an infinite number of ever decreasing distances in ever decreasing time (as opposed to constant amounts of time).
  - ColinWright 14y ago
    That's covered in the first part, where it defines an infinite sequence of time stamps leading up to midnight. It assumes each task can be completed in half the time of the one before, but if you're going to argue about that then don't bother thinking about infinity at all.

by mankyd 14y ago

ColinWright 14y ago

Article: "Case 1 says it might be infinitely many, case two says it might be none." > What? Case 2 says that all the balls will be put > back in. In both cases, there will be infinitely > many balls back in the barrel after midnight. Yes, and in case 2 there will be none outside, which is what's being asked. Quoting more completely: How many are outside of the barrel after midnight? We can't tell! Without being explicit, without actually naming the balls and saying which ones are being removed and replaced we simply cannot tell. Case 1 says it might be infinitely many, case two says it might be none. Case two has all the balls in the barrel after midnight. That means there are none outside, which is what's being asked. Or have I misunderstood you?

mankyd 14y ago
Ah, my mistake, you are correct. That being said, the example has another flaw: it is based on completing an infinite number of finite time tasks in finite time. That is to say, adding and removing an infinite number of balls will take an infinite amount of time, but we're only given an hour to do it in. Note that this is different from Zeno's paradox, wherein the two racers each have to move an infinite number of ever decreasing distances in ever decreasing time (as opposed to constant amounts of time).
- ColinWright 14y ago
  That's covered in the first part, where it defines an infinite sequence of time stamps leading up to midnight. It assumes each task can be completed in half the time of the one before, but if you're going to argue about that then don't bother thinking about infinity at all.