\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\def\thebestsuperhero{\textbf{Flash GORDON}}
\newcommand{\bestin}[2]{#1 is the best superhero in #2!}
\newcommand{\parenfrac}[2]{\left(\frac{#1}{#2}\right)}

\begin{document}

\section{Using \textbackslash def and \textbackslash newcommand}
\label{section-of-def-and-newcommand}

Facts:
\begin{enumerate} % use itemize instead of enumerate for bullet points
 \item My favorite superhero is \thebestsuperhero.
 \item \bestin{Spiderman}{Gotham City}
 \item We are currently in Section \ref{section-of-def-and-newcommand}.
 \item We will later see Equation \ref{eqn:ab}.
\end{enumerate}

\vspace{36pt}

\section{More Math}
Here's an equation that is \emph{labeled}: It is assigned a number,
\ref{eqn:ab}, that we can use to refer to it at any time.
\begin{equation}
 ( \frac{a+b}{a} )^n \leq e^{nb/a} . \label{eqn:ab}
\end{equation}

Here's an unlabeled one:
 \[ \left(1-\frac{x}{y}\right)^n \leq e^{n\frac{x}{y}} . \]

An array of equations that have optional labels, including Equation \ref{eqn:rs}:
\begin{align}
 \sum_{j=0}^{n-1} ar^j
   &= a\left(1 + r + r^2 + \dots\right) \nonumber \\
   &= a\parenfrac{1-r^n}{1-r}.          \label{eqn:rs}
\end{align}

An array of unlabeled equations as a Valentine's poem:
\begin{align*}
 x &= y          &\text{(given)} \\
 y &= z          &\text{(inferred)} \\
 z &= \text{you} &\text{(by Equation \ref{eqn:ab})} \\
 \text{you} &\heartsuit \text{me}.   &\text{(Lemma in \emph{The Heart Handbook})}
\end{align*}

\end{document}
