uses the word *Menge*.[^7] The English translation *set* can be misleading, because it refers to the Cantor’s conception of a set. The “set” is on a different “higher” level than its elements. [^8] Bolzano’s multitude, \[Menge\], is on the “same level” as the things it contains, because it is given by the usage of the connective “and”. Therefore, it is meaningful to speak about *parts* of a collection. These parts, however, are not subsets. Subsets are also on a “higher” level than their elements.

Bolzano introduces multitudes for the same reason as Cantor introduces sets. In order to capture an infinite plurality altogether, it must be collected in a single collection, a single, currently infinite, whole.

A special type of a multitude is *a plurality \[Vielheit\]*. Its parts are considered units of a certain kind $A$. (§4).

*A series \[Reihe\]* is also a collection of things, but unlike a multitude, it is ordered. Bolzano denotes things which the series contains as $A, B, C, \dots, L, M, N \dots $. We can always determine the following term $N$ of the series from the preceding term $M$ by the special *rule of formation* (§7).

If we have a series in which 