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 $��$ 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 $��$-monoidal}. We include some remarks on sets having cardinalities in $[-\infty,\infty]$.

This version points out erroneous examples in the published version. The examples are not necessary for the main thrust of the work