  The paper introduces the notion of the size of countable sets that preserves
the Part-Whole Principle and generalizes the notion of the cardinality of
finite sets. The sizes of natural numbers, integers, rational numbers, and all
their subsets, unions, and Cartesian products are algorithmically enumerable up
to one element as sequences of natural numbers. The method is similar to that
of Theory of Numerosities of Benci and Di Nasso 2019) but in comparison, it is
motivated by Bolzano's concept of infinite series from his Paradoxes of the
Infinite, it is constructive because it does not use ultrafilters, and set
sizes are uniquely determined. The results mostly agree with those of Theory of
Numerosities, but some differ, such as the size of rational numbers. However,
set sizes are just partially and not linearly ordered. \emph{Quid pro quo.}
