\documentclass[a4paper]{report}

\usepackage{glossary}

\makeglossary

\begin{document}

\pagenumbering{roman}
\printglossary

\chapter{Introduction}
\pagenumbering{arabic}

This is where I define the notation for a set $\mathcal{S}$
\glossary{name=set,description=a collection of objects}.

\clearpage

This is where I define the cardinality of a set $n(\mathcal{S})$
\glossary{name=cardinality,description=the number of objects within a set}

\clearpage

This is where I define the universal set $\mathcal{U}$
\glossary{name=universal set,description=the set containing everything}

\end{document}
