$$
%---- MACROS FOR SETS ----%
\newcommand{\znz}[1]{\mathbb{Z} / #1 \mathbb{Z}}
\newcommand{\twoheadrightarrowtail}{\mapsto\mathrel{\mspace{-15mu}}\rightarrow}
% popular set names
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\I}{\mathbb{I}}
% popular vector space notation
\newcommand{\V}{\mathbb{V}}
\newcommand{\W}{\mathbb{W}}
\newcommand{\B}{\mathbb{B}}
\newcommand{\D}{\mathbb{D}}
%---- MACROS FOR FUNCTIONS ----%
% linear algebra
\newcommand{\T}{\mathrm{T}}
\renewcommand{\ker}{\mathrm{ker}}
\newcommand{\range}{\mathrm{range}}
\renewcommand{\span}{\mathrm{span}}
\newcommand{\rref}{\mathrm{rref}}
\renewcommand{\dim}{\mathrm{dim}}
\newcommand{\col}{\mathrm{col}}
\newcommand{\nullspace}{\mathrm{null}}
\newcommand{\row}{\mathrm{row}}
\newcommand{\rank}{\mathrm{rank}}
\newcommand{\nullity}{\mathrm{nullity}}
\renewcommand{\det}{\mathrm{det}}
\newcommand{\proj}{\mathrm{proj}}
\renewcommand{\H}{\mathrm{H}}
\newcommand{\trace}{\mathrm{trace}}
\newcommand{\diag}{\mathrm{diag}}
\newcommand{\card}{\mathrm{card}}
\newcommand\norm[1]{\left\lVert#1\right\rVert}
% differential equations
\newcommand{\laplace}[1]{\mathcal{L}\{#1\}}
\newcommand{\F}{\mathrm{F}}
% misc
\newcommand{\sign}{\mathrm{sign}}
\newcommand{\softmax}{\mathrm{softmax}}
\renewcommand{\th}{\mathrm{th}}
\newcommand{\adj}{\mathrm{adj}}
\newcommand{\hyp}{\mathrm{hyp}}
\renewcommand{\max}{\mathrm{max}}
\renewcommand{\min}{\mathrm{min}}
\newcommand{\where}{\mathrm{\ where\ }}
\newcommand{\abs}[1]{\vert #1 \vert}
\newcommand{\bigabs}[1]{\big\vert #1 \big\vert}
\newcommand{\biggerabs}[1]{\Bigg\vert #1 \Bigg\vert}
\newcommand{\equivalent}{\equiv}
\newcommand{\cross}{\times}
% statistics
\newcommand{\cov}{\mathrm{cov}}
\newcommand{\var}{\mathrm{var}}
\newcommand{\bias}{\mathrm{bias}}
\newcommand{\E}{\mathrm{E}}
\newcommand{\prob}{\mathrm{prob}}
\newcommand{\unif}{\mathrm{unif}}
\newcommand{\invNorm}{\mathrm{invNorm}}
\newcommand{\invT}{\mathrm{invT}}
\newcommand{\P}{\text{P}}
\newcommand{\pmf}{\text{pmf}}
\newcommand{\pdf}{\text{pdf}}
% real analysis
\renewcommand{\sup}{\mathrm{sup}}
\renewcommand{\inf}{\mathrm{inf}}
%---- MACROS FOR ALIASES AND REFORMATTING ----%
% logic
\newcommand{\forevery}{\ \forall\ }
\newcommand{\OR}{\lor}
\newcommand{\AND}{\land}
\newcommand{\then}{\implies}
% set theory
\newcommand{\impropersubset}{\subseteq}
\newcommand{\notimpropersubset}{\nsubseteq}
\newcommand{\propersubset}{\subset}
\newcommand{\notpropersubset}{\not\subset}
\newcommand{\union}{\cup}
\newcommand{\Union}[2]{\bigcup\limits_{#1}^{#2}}
\newcommand{\intersect}{\cap}
\newcommand{\Intersect}[2]{\bigcap\limits_{#1}^{#2}}
\newcommand{\intersection}[2]{\bigcap\limits_{#1}^{#2}}
\newcommand{\Intersection}[2]{\bigcap\limits_{#1}^{#2}}
\newcommand{\closure}{\overline}
\newcommand{\compose}{\circ}
% linear algebra
\newcommand{\subspace}{\le}
\newcommand{\angles}[1]{\langle #1 \rangle}
\newcommand{\identity}{\mathbb{1}}
\newcommand{\orthogonal}{\perp}
\renewcommand{\parallel}[1]{#1^{||}}
% calculus
\newcommand{\integral}[2]{\int\limits_{#1}^{#2}}
\newcommand{\limit}[1]{\lim\limits_{#1}}
\newcommand{\approaches}{\rightarrow}
\renewcommand{\to}{\rightarrow}
\newcommand{\convergesto}{\rightarrow}
% algebra
\newcommand{\summation}[2]{\sum\nolimits_{#1}^{#2}}
\newcommand{\product}[2]{\prod\limits_{#1}^{#2}}
\newcommand{\by}{\times}
\newcommand{\integral}[2]{\int_{#1}^{#2}}
\newcommand{\ln}{\text{ln}}
% exists commands
\newcommand{\notexist}{\nexists\ }
\newcommand{\existsatleastone}{\exists\ }
\newcommand{\existsonlyone}{\exists!}
\newcommand{\existsunique}{\exists!}
\let\oldexists\exists
\renewcommand{\exists}{\ \oldexists\ }
% statistics
\newcommand{\distributed}{\sim}
\newcommand{\onetoonecorresp}{\sim}
\newcommand{\independent}{\perp\!\!\!\perp}
\newcommand{\conditionedon}{\ |\ }
\newcommand{\given}{\ |\ }
\newcommand{\notg}{\ngtr}
\newcommand{\yhat}{\hat{y}}
\newcommand{\betahat}{\hat{\beta}}
\newcommand{\sigmahat}{\hat{\sigma}}
\newcommand{\muhat}{\hat{\mu}}
\newcommand{\transmatrix}{\mathrm{P}}
\renewcommand{\choose}{\binom}
% misc
\newcommand{\infinity}{\infty}
\renewcommand{\bold}{\textbf}
\newcommand{\italics}{\textit}
\newcommand{\step}{\text{step}}
$$
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