Are These Containers
Full or Empty?
An Experimental Investigation of Infinity
Infinity is a very strange concept to most people.
Most people do not ever encounter a problem in which they have to work
with infinity and therefore do not have much real-life experience to relate
to when encountering problems such as this.
You might be surprised to find that
the first container is indeed empty
This is why:
When you continue the process forever, is there a single number that you
can say with 100% certainty
will be left in the box? The answer is
no. This may seem strange but it can be proven by finding
probability that a specific number is in the box. This is a very
mathematical process to prove but here I will summarize.
Since we are working with an infinite number of numbers,
we would need to use the formula for infinite sums. By finding the
probably of any one of the numbers, since they are equally likely because
each only occurs once, and using the formula of infinite sums, the sum converges
The second container is full.
This is why:
If you though about the process, couldn't you state a number that would be
in the container? As a matter of fact, there are many numbers because
only the multiples of 10 will be missing. So the number 1, 2, 3, and so on,
are all numbers that are in the containers. The mathematical process is the
same as before except that you will find that the infinite sum of the probabilities
will converge to one. So there is a 100% chance that you will find an infinite
number of numbers in the container.