the first term is a unit of the $A$ kind and every following term is derived from the previous one as a sum of its predecessor and a new unity of the kind $A$, then all of the terms of this series are *pluralities*, or, more straightforwardly, *numbers.* (§8). Some pluralities have so many terms, that they exhaust all the units and they have no last term.

Now it is more evident why Bolzano defines a collection as a whole consisting of certain parts. A series is an example of such a whole. Its sum is a quantity of the same kind, it is a sum of all its parts.

A plurality is called *infinite* if it is greater than every finite plurality, i.e. if every finite multitude represents only a part of it. (§9).

*A finite multitude* is not explicitly defined here. We find the explanation in §22. The numbers of its parts are equal to some natural number $n$.

> If we know that $A$ is finite, we designate some arbitrary thing in the multitude $A$ by 1, some other multitude by 2, etc. …, we must sometimes arrive at a thing in $A$ after which nothing remains 