\documentclass[12pt,reqno,twoside,usenames,dvipsnames]{amsart}

\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{mathabx}
\usepackage{hyperref}
\usepackage{verbatim}
\hypersetup{breaklinks=true,
pagecolor=white,
colorlinks=true,
linkcolor= blue,
hyperfootnotes= true,
urlcolor=blue
}
\urlstyle{rm}

 

\newcommand{\margincomment}[1]
  {\mbox{}\marginpar{\tiny\hspace{0pt}#1}}

\newcommand{\comments}[1]{}
\renewcommand{\baselinestretch}{1.2}
 \parindent 24pt
 \parskip 10pt
\reversemarginpar
\topmargin -1in \oddsidemargin -.5in \evensidemargin -.5in
\textheight 10in \textwidth 7in


\begin{document}
 \begin{Huge}
\noindent
Eric Rasmusen\\
November 7, 2021
\begin{center}

{\large {\bf  Handout: Order Symbols
}}
\end{center}
 

  $ x  \in  [3,5)$ means $x:  x\geq 3 $ and $x <5$.  Thus, $x$ could equal 3, or 3.001, or 4.2, or 4.9999, but not 5. 

$x \in \{3, 5\}$ means $x$ is either 3 or 5, but not anything in between. 

An open dot on a number line means that number is not included. A closed dot means that number *is* included. 

An interval is a set of numbers in between two end point numbers. Thus, the interval [3,5] includes 3, 3.0000001, 3.23, 4.01, 4.5, 4.999, 5, and all the other numbers in between. 

We say that $[3,5]$ is a Closed Interval, because it includes its end points, 3 and 5. 

We say that $(3,5)$ is an Open Interval, because it doesn't included its end points, 3 and 5. 

  

\end{Huge}
 
 \end{document}
