When I was an undergraduate, I had this thought: Suppose that everything is made of atoms (I mean, pieces which cannot be separated further) and the universe has a finite amount of space.
Let $N$ be the total number of atoms in the universe, $V$ the total space of the universe and $v$ the volume of every atom. For every atom there are at most $\frac{V}{v}$ possible placements inside the universe, so all the possible ways to place all atoms inside the universe is at most $\bigl(\frac{V}{v}\bigr)^N$.
This number is clearly $<\infty$ which means that an infinite number of times everything in the universe is placed exactly in the same place.
(Which means that if we wait for many, many years, we could probably see an infinite number of times Bolt winning at the Olympic games, setting a "new" world record at $9.58$ seconds)
My question is:
Is it true that (based on the arguments above) one of the following propositions must hold true?
Not everything is made of atoms.
The universe's space is infinite.
An infinite number of times, everything in the universe is placed exactly in the same place.
- Note : I consider quantum matter (non - continious situation - positions)