\documentclass[11pt]{article}
\usepackage{mycommands}
\date{Due Tuesday, 2/12}
\title{Math 104 Homework 1 (Vaintrob)}
\author{}
\begin{document}
\maketitle
\section{Exercises 7.1, 7.2} 

\section{Exercise 7.3} (a), (c), (e), (i)

\section{Exercise 8.1}

\section{Exercise 8.2} 

\section{Exercise 8.3}

\section{Exercise 8.4}

\section{Exercise 8.5}

\section{Challenge problem} You can choose to do this instead of any three of the above.

This problem assumes knowledge of the formal definition of what it means for a function to be continuous (17.1 in the book). 

Show that a sequence $s_1, s_2, \dots$ is convergent with limit $s_\infty$ if and only if the function $f(x)$ is continuous at $0$, with $f(x)$ defined as follows:
$$f(x) =
\begin{cases}
  s_1, & 1\le x\\
  s_\infty, & x \le 0 \\
  s_n, & n\ge 2\text{ and }1/n \le x<1/(n-1)
  \end{cases}
$$
\end{document}