enough that we can derive the rules. Bolzano makes an important assumption that all series have *one and the same multitude of terms*. (§33). He does not ask what the plurality of the terms is, but assumes it is *always the same.* The sum of the series represents a whole, a uniquely given quantity. If we add positive terms, then the quantity increases; if we take away positive terms, the quantity decreases.

It is similar when we consider the sum of the series $$1/2 + 1/4 + 1/8 + \dots + \text{in inf.}$$ We are not interested in the plurality of the terms, but we are interested in its sum, which is equal to $1$.[^14]

\[rady\]Bolzano introduces several examples of infinite series (§29, §33).

1.  $N = 1 + 1 + 1 + 1 + \dots + \text{in inf.} $

2.  $P = 1 + 2 + 3 + 4 + \dots + \text{in inf.} $

3.  $S = 1 + 4 + 9 + 16 + \dots + \text{in inf.} $

4.  $N_n = \dots 1 + 1 + 1 + \dots + \text{in inf.} $

    The last series is similar to the first one, but we only add 