It is late and I feel like I am confusing myself. So O is composed of n atoms. So how many parts does n have? I can think of it two ways:

1. We remove one arbitrary atom from O. There are here n possibilities. We can then remove another arbitrary atom from O. There are here n-1 possibilities. We repeat this procedure n times. Doing this for any possible combination of atoms should get us through all permutations. This would mean that there are n! parts of O.

2. We take the set of atoms in O. This will have cardinality n. We then take the powerset of this set, which will give us all possible combinations of parts of O. This will have cardinality 2^n.

I can't for the life of me figure out which is correct right now, lol. Can somebody help me out please!