Skip to main content ☰ Contents You! < Prev ^ Up Next > \(\require{cancel}\require{upgreek} \newcommand{\ds}{\displaystyle}
\renewcommand{\textcolor}[2]{{\color{#1}{#2}}}
\newcommand{\es}{ {\varnothing}}
\newcommand{\st}{ \;\mathrm{s.t.}\; }
\newcommand{\so}{ \;\mid\; }
\newcommand{\pow}[1]{ \mathcal{P}\left(#1\right) }
\newcommand{\set}[1]{ \left\{#1\right\} }
\renewcommand{\neg}{\sim}
\newcommand{\rel}[1][R]{\;\mathcal{#1}\;}
\newcommand{\nrel}[1][R]{\;\cancel{\mathcal{#1}}\;}
\newcommand{\dee}[1]{\mathrm{d}#1}
\newcommand{\diff}[2]{\dfrac{\mathrm{d}#1}{\mathrm{d}#2}}
\renewcommand{\mod}[1]{\ (\mathrm{mod}\ #1)}
\newcommand{\lcm}{\mathrm{lcm}}
\let\oldepsilon\epsilon
\renewcommand{\epsilon}{\varepsilon}
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 8 Return to sets
As we mentioned early, we have changed the order of topics a little in this text so that we can get to proving things as quickly as possible and get you more comfortable with basic proof methods. This meant that we skipped several basic aspects of sets that we should now cover. Thankfully we can now do a bit more with these basic bits of set theory — indeed we can prove some things!
