Suppose you have a bottle with infinite volume and infinite number of balls. Now it's 11 o'clock and an hour left till 12.
So you put 10 balls in and take one out 30 minutes later. You repeat this 15 minutes later. Then 7.5 and so on.
Basically repeat that every (Remaining time) / 2
How many balls are in the bottle at 12 o'clock?
My first thought was infinite but no.
Then i thought it will never be 12 o'clock. Like the Heracles and turtle example. Obviously no.
Now Another approach. If we consider the set of natural numbers and the set of even numbers. They have equal power or in other words equal "length" whatever that means. Taking the same approach here, infinite number of adding 10 and infinite number of subtracting 1 have equal powers so. There are no balls in the bottle at 12 o'clock ??
What is infinite - infinite ?
Despite the sets if they have equal powers then difference is always 0?
I would like to know everything about this. Every detail. Answer to the question is not the most important here.