  After reviewing a universal characterization of the extended positive real
numbers published by Denis Higgs in 1978, we define a category which provides
an answer to the questions: \begin{itemize} \item what is a set with half an
element? \item what is a set with $\pi$ elements? \end{itemize} The category of
these extended positive real sets is equipped with a countable tensor product.
We develop somewhat the theory of categories with countable tensors; we call
the commutative such categories {\em series monoidal} and conclude by only
briefly mentioning the non-commutative possibility called {\em
$\omega$-monoidal}. We include some remarks on sets having cardinalities in
$[-\infty,\infty]$.
