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(6): Respectfully, I disagree with all (save perhaps eric) by FatBoy)
Dude!
No one's trying to make this personal. We were explaining "the basics of this kind of problem" only because you seem(ed) to be unfamiliar with it.
Now... that aside... you continue to make statements that ARE non sequiturs. You say, "The simple fact is... all of that thought does not apply." But... it does!
(And I think Bryan and I imagine that some other people around here might be silently reading this thread and might want to see it come to a logical, coherent resolution.)
_________________
You are correct that at the end of the minute, we stop moving marbles around. At this point in time, we have a set of marbles that have been placed in the jar and a set that have been in and have come back out.
Now... the whole problem revolves around identifying the difference between the contents of those two sets. (BTW, I've not limited the set in any way. The sets are what they are after the minute has expired.)
The content of either set is not necessarily finite, though you continue to claim it is (for a reason that continues to escape me). But I agree, that it will not change (for we are no longer performing operations that affect the contents of either set).
As stated previously, in case (A), the contents of the two sets are not the same, and leaves an infinite number of marbles in the bag. And in case (B), the contents of the two sets are the same, and therefore each marble that has been placed in the bag has been removed, so the bag is empty.
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Lastly, you are correct, in that you cannot COUNT the integers (by your implied definition of counting). But you CAN map them to another set of the same Cardinality.
Cheers
--- SK
P.S. I hope we can continue to keep the discussion related to the topic at hand. :-)
Edited on September 9, 2003, 3:01 pm
re(7): Respectfully, I disagree with all (save perhaps eric)
