\documentclass{beamer}

\usepackage{amsmath, amssymb, amsthm}
%\usepackage{hyperref}


\usetheme{boxes}
\usecolortheme{seagull}
\definecolor{background}{gray}{.95}
\setbeamercolor{normal text}{bg=background}
\setbeamertemplate{navigation symbols}{}


\author{Logan Axon}
\institute{Gonzaga University}
\date{\today}
\title{Logic basics}

\newtheorem{thm}{Theorem}
\theoremstyle{definition}
\newtheorem{dfn}{Definition}
\newtheorem{exercise}{Exercise}
\newtheorem{idea}{Idea}
\newtheorem{question}{Question}
\newtheorem{conjecture}{Conjecture}

\newcommand{\NN}{\mathbb{N}} % natural numbers
\newcommand{\ZZ}{\mathbb{Z}} % integers
\newcommand{\QQ}{\mathbb{Q}} % rational number
\newcommand{\RR}{\mathbb{R}} % real numbers

\newcommand{\pow}{\mathcal{P}} % power set


\begin{document}
%%%%%%
\begin{frame}{TFAE}

\begin{thm}
Let $f$ be a function on $\RR$ such that $\displaystyle \lim_{x \to \infty} \left[ \frac{f(x)}{x} \right]$ exists.
The following are equivalent:
\begin{enumerate}
\item $\displaystyle \lim_{x \to \infty} \left[ \frac{f(x)}{x} \right] = 1$
\item $\displaystyle \lim_{x \to \infty} \left[ \frac{x}{f(x)} \right] = 1$
\item $\displaystyle \lim_{x \to \infty} \left[ \frac{f(x)}{x} \right] \leq 1$ and $\displaystyle \lim_{x \to \infty} \left[ \frac{x}{f(x)} \right] \leq 1$
\end{enumerate}
\end{thm}


This means $1 \iff 2$ and $1 \iff 3$ and $2 \iff 3$.

\pause

\begin{question}
Do we have to do 6 proofs?
\end{question}

\end{frame}

\end{document}