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(4): more by Cory Taylor)
I'm sorry Cory.
As n approaches (and we've conceded, reached) infinity...
No Cory, no one has conceded that any iterative process REACHES infinity. You simply want to justify your point.
You cannot say your math is flawed without showing what the flaw is (at least not and still be taken seriously). There is no flaw in the reasoning behind the solution to this problem. And you continue to be unable to show what it is.
There is nothing in this solution that is "out of reach" of your facilities, and I'm sure you are familiar with set notation (though you seem eager to avoid discussing it).
What's more, one most certainly can demonstrate that the SIZE of some infinities is definitely larger than others (size of real numbers > size of rational numbers), whereas the SIZE of some infinities is equal to some others (size of rational numbers = size of integers).
I will FOR A THIRD TIME suggest that you address the issue as membership in a set, and mappings from one set onto another. And you will, more than likely, continue to avoid this way of analyzing the problem, because it supports the solution.
re(5): more
