Abstract
?  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}
That is, we categorify (or objectify) the monoid $[0,\infty]$ under addition.
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}.
We may include some remarks on sets having cardinalities in $[\infty,\infty]$.
This is joint work with George Janelidze.

