% use [nosolutions] flag to hide solutions. % use [solutions] flag to show solutions. \documentclass[ solutions, singlenumbering ]{./ormc_handout} \title{The Size of Sets} \subtitle{Prepared by Mark on \today{}} \begin{document} \maketitle \section{Set Basics} \definition{} A \textit{set} is a collection of objects. \par If $a$ is an element of set $S$, we write $a \in S$. This is pronounced \say{$a$ in $S$.} \par The position of each element in a set or the number of times it is repeated doesn't matter. \par All that matters is \textit{which} elements are in the set. \vspace{2mm} We say two sets $A$ and $B$ are equal if every element of $A$ is in $B$, and every element of $B$ is in $A$. This is known as the \textit{principle of extensionality.} \problem{} Convince yourself that $\{a, b\} = \{b, a\} = \{a, b, a, b, b\}$. \begin{solution} This is a solution. \end{solution} \end{document}