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+% This file is public domain. See the "Examples" chapter
+% in the bib2gls user manual for a more detailed description
+% of this file.
+
+\documentclass[a4paper]{article}
+
+\usepackage[T1]{fontenc}
+\usepackage{amssymb}
+
+\usepackage[colorlinks]{hyperref}
+\usepackage[record,% using bib2gls
+ nostyles,% don't load default styles
+ postdot,% append a dot after descriptions
+ stylemods={mcols},% load glossary-mcols.sty and patch
+ style=mcolalttree]{glossaries-extra}
+
+\GlsXtrLoadResources[
+ src={no-interpret-preamble},
+ interpret-preamble=false
+]
+
+\GlsXtrLoadResources[
+ src={interpret-preamble,bigmathsymbols,mathsobjects},
+ sort-field={category},
+ identical-sort-action={description},
+ field-aliases={identifier=category,format=user1},
+ replicate-fields={category=group},
+ set-widest,
+ save-locations=false
+]
+
+\renewcommand{\GlsXtrFmtDefaultOptions}{}
+
+% requires glossaries-extra.sty v1.23+
+\newcommand{\set}[2][]{\glsxtrfmt*[#1]{set}{#2}}
+\newcommand{\nlset}[1]{\glsxtrentryfmt{set}{#1}}
+\newcommand*{\setcontents}[2][]{\glsxtrfmt*[#1]{setcontents}{#2}}
+\newcommand*{\setmembership}[2]{\glsxtrfmt*{setmembership}{{#1}{#2}}}
+\newcommand*{\setcard}[2][]{\glsxtrfmt*[#1]{setcard}{#2}}
+\newcommand*{\nlsetcard}[1]{\glsxtrentryfmt{setcard}{#1}}
+\newcommand*{\transpose}[2][]{\glsxtrfmt*[#1]{transpose}{#2}}
+\newcommand*{\nltranspose}[1]{\glsxtrentryfmt{transpose}{#1}}
+\newcommand*{\inv}[2][]{\glsxtrfmt*[#1]{inverse}{#2}}
+\newcommand*{\nlinv}[1]{\glsxtrentryfmt{inverse}{#1}}
+\newcommand*{\Vtr}[2][]{\glsxtrfmt[#1]{vector}{#2}}
+\newcommand*{\nlVtr}[1]{\glsxtrentryfmt{vector}{#1}}
+\newcommand*{\Mtx}[2][]{\glsxtrfmt[#1]{matrix}{#2}}
+\newcommand*{\nlMtx}[1]{\glsxtrentryfmt{matrix}{#1}}
+
+\begin{document}
+\section{Sets}
+The universal set ($\gls{universalset}$) contains everything.
+The empty set ($\gls{emptyset}$) contains nothing.
+Some assignments:
+\[
+ \set{B}[_1] = \setcontents{1, 3, 5, 7},\quad
+ \set{B}[_2] = \setcontents{2, 4, 6, 8},\quad
+ \set{B}[_3] = \setcontents{9, 10}
+\]
+Define:
+\[\set{A} = \gls{bigcup}[_{i=1}^3] \set{B}[_i]
+= \setcontents{1, \ldots, 10} \]
+The cardinality of a set \gls{set} is denoted \gls{setcard}
+and is the number of elements in the set.
+\[
+ \setcard{\nlset{B}_1} = 4,\quad
+ \setcard{\nlset{B}_2} = 4,\quad
+ \setcard{\nlset{B}_3} = 2,\quad
+ \setcard{\nlset{B}_1\cup\nlset{B}_2} = 8,\quad
+ \nlsetcard{\gls{emptyset}} = 0
+\]
+
+\section{Spaces}
+A number space (denoted $\gls{numberspace}$) is characterised
+by a set of entities with a set of axioms. For example:
+\begin{align*}
+\gls{naturalnumbers}
+ &= \setmembership{x}{x\text{ is positive integer}}\\
+\gls{integernumbers}
+ &= \setmembership{x}{x\text{ is an integer}}\\
+\gls{realnumbers}
+ &= \setmembership{x}{x\text{ is a real number}}
+\end{align*}
+
+\section{Vectors and Matrices}
+
+A matrix (denoted \gls{matrix}) is a rectangular array of values.
+A vector (denoted \gls{vector}) is a column or row of values (that
+is a one-dimensional matrix).
+\[
+ \gls{identitymatrix}\Vtr{x} = \Vtr{x},\quad
+ \Mtx{A}\inv{\nlMtx{A}} = \gls{identitymatrix},\quad
+ \inv{\nlVtr{x}}\gls{1vec} = \gls{sum}[_i] x_i
+\]
+
+\printunsrtglossaries
+\end{document}