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
Defining Infinity by Brian Smith)
Brian, you said:
"Call the base unit of infinity w."
"We can define this instance of infinity as w."
*** Two different definitions of infinity. This is a problem
Also, you DEFINE "2*w>w+1>w".... this ALSO is a problem. You seem to be thinking of w as an integer. But I'm not certain about what's going on in your head. Infinity is not an integer, nor is it a real number.... Generally, infinities (at least in common, not -"Brian Smith defined infinities") are dealt with as the size of sets.
If you can create a one-to-one mapping (ANY one-to-one mapping) from one infinity to another, then they have the same size. This does NOT mean that they are equal. But it DOES mean they are equal in size. (A simple example is... are there more points on the line segment from (0,1) or from (2,4), both on a one dimensional axis). Since I can create a (trivial) mapping from one to the other, they have the same size (cardinality).
re: Defining Infinity
