To have a whole made of parts requires at least three things: the whole, one part, and another part.
The whole must be distinct from each of the parts, i.e. it must not be one of the parts, since if the whole were the part, the part would not be a part, but the whole. Likewise each of the parts must be distinct from one another.
On other other hand, if there was no other relationship between the parts and the whole, we would simply be talking about three unrelated things. In order for the parts to be parts, they must be something of the whole. The part thus expresses something of the existence of the whole, a mode of its existence, but not its existence overall. Thus for example body and soul are aspects of a man, but neither is the man overall.
In order to be a whole, therefore, a thing must exist in three ways: as itself, as something which it is not, and as something else which it is not. Each of these three must be distinct from the other two.
The whole is greater than the part insofar as the whole exists not only as that part (which of itself would cause equality), but also as itself and as the other part.