\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb,hyperref,enumitem,amsthm}

%\usepackage[margin=1.0in]{geometry}

\theoremstyle{theorem}
\newtheorem{theorem}{Theorem}

\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}

\author{Sherwood Hachtman}
\title{Assignment 2}
\date{Math 300 -- Spring 2019}

\begin{document}
\maketitle
The second homework assignment has two parts:
  \begin{enumerate}
    \item Revise the Theorem and Proof activity, "Day 1: Sets of Ages", posted on the main web page.  You will need to fill in details and clarify the exposition.  In particular:
      \begin{itemize}
        \item Introduce names for the objects (sets, etc.) you consider.  Here you might employ {\LaTeX} notation for a function $f:A \to B$, or for an indexed sum $\sum_{i \in I} a_i$.  A separately displayed line of math looks like:
          \[
            \sum_{i \in I} a_i \leq N.
          \] 
        \item Use the \texttt{theorem} environment to organize your assignment as definitions/examples/theorems/proofs, separated by exposition where appropriate (see below for examples).
        \item Cite the pigeonhole principle in your proof, and say what function you are applying it to;
        \item Say why the sets you obtain in the conclusion of the proof are disjoint.
  \end{itemize}

   \item Consider variants of the theorem where the number of people is some $n< 10$ (but the age range is still from 0 to 100).  Is it true with $n=9$?  $n=8$?  Figure out the largest $n$ for which it fails, and give a counterexample.  
   
   Optional (extra credit): Find a more general theorem that allows the age range to be variable (i.e. from 0 to $a$ for some integer $a$) and prove it.
   \end{enumerate}
   
   You are required to use the \texttt{theorem} environment in this assignment.  Look online, or see the examples below in the \texttt{.tex} source file for this document, for help.  
     \begin{theorem} A theorem is a hopefully interesting mathematical statement.
     \end{theorem}
     \begin{proof} Its proof would look like this. \end{proof}
     An example showing the theorem does not generalize:
     \begin{example} 
       Might look like this.
     \end{example}
   Note these were typeset differently (italics vs.\ not); this was because we used different \texttt{theoremstyle}s in the preamble of this document (see lines 7-12 above).
\end{document}