% \documentclass tells what type of document you are preparing.
% ''article'' is the most generic type and works for anything you'll be doing
\documentclass{article}
% \usepackage imports packages with new symbols
% There are LOTS of possible packages, but the ones below cover most everything
% you'll need for math and graphics.
\usepackage{amsmath,amsthm,amssymb,latexsym,graphicx}
% \newtheorem lets you name a few different kinds of theorem environments
% The first argument is what you want the command to be named.
% The second argument is the word that should actually appear in the document.
\newtheorem*{thm}{Theorem}
\newtheorem*{prop}{Proposition}
\newtheorem*{defn}{Definition}
\newtheorem*{lem}{Lemma}
\newtheorem*{cor}{Corollary}
\newtheorem*{conj}{Conjecture}
% Put your title, author, and date information BEFORE \begin{document},
% then call the \maketitle command immediately after \begin{document}
\title{Math 4980 Homework 1}
\author{Austin Mohr}
\date{\today} % You can specify a date, or just use \today to use today's date.
% \begin{document} and \end{document} mark the beginning and end of the
% part of the document you actually want to be typeset
\begin{document}
% \maketitle takes all the title, author, and date information and makes
% a nice looking header for the document
\maketitle
% Finally, we'll start typing the body of our document.
% This tells the compiler that I'm getting ready to type a theorem.
% I think ``Proposition'' sounds less pretentious than ``Theorem'' for a homework assignment.
% Notice I've tried to write the statement to sound like a proposition rather than an imperative
% by leaving out words like ``prove''.
\begin{prop}
Any subset of size $n+1$ chosen from the set $\{1, 2, 3, \dots, 2n\}$ will contain a pair of relatively prime numbers.
\end{prop}
% This tells the compiler that I'm getting ready to type a proof.
\begin{proof}
Proof goes here.
\end{proof}
% Here's the end of the document
\end{document}