A molecule is a collection of one or more atoms. A hydrogen molecule is the smallest possible molecule consisting of one hydrogen atom. Most of the molecules we come across in our day to day lives are bigger than that. Atoms are fun to talk about because they are extroadinarly small, amd make up everything.
Database theorists would say that there is a one to many relation between molecules and atoms.
Assuming that there were an infinite number of atoms, a transfinite theorist would say that the number of atoms equals the number of molecules. Their claim is based on the fact that if you began comparing molecules to atoms, you would not run out of the former before your ran out of the latter. Both sets are infinite.
I understand that physicists believe there is a finite number of atoms in this universe. However, some theorists contend that there is an infinite number of universes. This adds as new dimension to the comparison of atoms to molecules.
Yes, we would run out of molecules before we ran out of atoms in this universe...but we could always shift dimensions and start pulling atoms from another universe.
Assuming that all the universes are basically the same size, we would exhaust the molecule supply in several universes before counting all of our atoms in this universe. This deficit should continue on during our inventory...yet...somehow when we reach the completed infinity, the atoms and molecule count is supposed to come out the same.
That one to many relations turn into one to one correspondences is still the most incredible thing about transfinite theory. Thinking on the scale of atoms and universes simply makes the magnitude of the claim more grandeous, yet is not a true paradox. We'll get to those next.