Set Theory in LaTeX
I hate the lack of syntax in a lot of LaTeX math, especially now that I’ve started typing my notes and problem sets in two classes that are all set theory. Think about it, syntactically I am entering the symbol for set union, so why should I call it \cup? I shouldn’t. Thus, I have put together a whole heaping helping of set theory commands that I use all the time. If you want to see the kind of notes I’m making, head over here.
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amsfonts}
\theoremstyle{definition}% default
\newtheorem{prop}{Proposition}[enumii]
\theoremstyle{definition}
\newtheorem*{Proof}{Proof}
\theoremstyle{remark}
\newtheorem{case}{Case}[prop]
%%%%%%This is where I put in math commands
\renewcommand{\implies}{\ensuremath{\to}}%the normal implies arrow is double width, so this makes it thinner
%particular sets
\newcommand{\naturals}{\ensuremath{\mathbb{N}}}
\newcommand{\integers}{\ensuremath{\mathbb{Z}}}
\newcommand{\rationals}{\ensuremath{\mathbb{Q}}}
\newcommand{\reals}{\ensuremath{\mathbb{R}}}
%words
\renewcommand{\iff}{\ensuremath{\operatorname{iff}}}
%\renewcommand{\st}{\ensuremath{\operatorname{s.t.\ }}}
%\DeclareMathOperator{\st}{s.t.\ }
%logic
\newcommand{\nd}{\ensuremath{\operatorname{and}}}
\newcommand{\ro}{\ensuremath{\operatorname{or}}}
\DeclareMathOperator{\then}{then}
\DeclareMathOperator{\but}{but}
%set operators
\newcommand{\set}[1]{\left\{#1\right\}}
\newcommand{\ordered}[1]{\left(#1\right)}
\let\propsubset\subset
\renewcommand{\subset}{\subseteq}
\let\propsupset\supset
\renewcommand{\supset}{\supseteq}
\newcommand{\intersect}{\cap}
\newcommand{\union}{\cup}
\newcommand{\symdif}{\vartriangle}
\newcommand{\complementset}[2][]{\ensuremath{\mathcal{C}_{#1} \left(#2\right)}}
\newcommand{\powerset}[1]{\ensuremath{\mathscr{P}\left(#1\right)}}
\newcommand{\cartesian}{\ensuremath{\times}}
