% ┌                                                ┐
% │                      Math                      │
% └                                                ┘

% BB shortcuts (for number spaces, etc)
\newcommand{\A}{\ensuremath{\mathbb{A}}}
\newcommand{\B}{\ensuremath{\mathbb{B}}}
\newcommand{\C}{\ensuremath{\mathbb{C}}}
\newcommand{\D}{\ensuremath{\mathbb{D}}}
\newcommand{\E}{\ensuremath{\mathbb{E}}}
\newcommand{\F}{\ensuremath{\mathbb{F}}}
\newcommand{\G}{\ensuremath{\mathbb{G}}}
\renewcommand{\H}{\ensuremath{\mathbb{H}}}
\newcommand{\I}{\ensuremath{\mathbb{I}}}
\newcommand{\J}{\ensuremath{\mathbb{J}}}
\newcommand{\K}{\ensuremath{\mathbb{K}}}
\renewcommand{\L}{\ensuremath{\mathbb{L}}}
\newcommand{\M}{\ensuremath{\mathbb{M}}}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\renewcommand{\O}{\ensuremath{\mathbb{O}}}
\renewcommand{\P}{\ensuremath{\mathbb{P}}}
\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\renewcommand{\S}{\ensuremath{\mathbb{S}}}
\newcommand{\T}{\ensuremath{\mathbb{T}}}
\newcommand{\U}{\ensuremath{\mathbb{U}}}
\newcommand{\V}{\ensuremath{\mathbb{V}}}
\newcommand{\W}{\ensuremath{\mathbb{W}}}
\newcommand{\X}{\ensuremath{\mathbb{X}}}
\newcommand{\Y}{\ensuremath{\mathbb{Y}}}
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}

% Caligraphic
\newcommand{\cA}{\ensuremath{\mathcal{A}}}
\newcommand{\cB}{\ensuremath{\mathcal{B}}}
\newcommand{\cC}{\ensuremath{\mathcal{C}}}
\newcommand{\cD}{\ensuremath{\mathcal{D}}}
\newcommand{\cE}{\ensuremath{\mathcal{E}}}
\newcommand{\cF}{\ensuremath{\mathcal{F}}}
\newcommand{\cG}{\ensuremath{\mathcal{G}}}
\newcommand{\cH}{\ensuremath{\mathcal{H}}}
\newcommand{\cI}{\ensuremath{\mathcal{I}}}
\newcommand{\cJ}{\ensuremath{\mathcal{J}}}
\newcommand{\cK}{\ensuremath{\mathcal{K}}}
\newcommand{\cL}{\ensuremath{\mathcal{L}}}
\newcommand{\cM}{\ensuremath{\mathcal{M}}}
\newcommand{\cN}{\ensuremath{\mathcal{N}}}
\newcommand{\cO}{\ensuremath{\mathcal{O}}}
\newcommand{\cP}{\ensuremath{\mathcal{P}}}
\newcommand{\cQ}{\ensuremath{\mathcal{Q}}}
\newcommand{\cR}{\ensuremath{\mathcal{R}}}
\newcommand{\cS}{\ensuremath{\mathcal{S}}}
\newcommand{\cT}{\ensuremath{\mathcal{T}}}
\newcommand{\cU}{\ensuremath{\mathcal{U}}}
\newcommand{\cV}{\ensuremath{\mathcal{V}}}
\newcommand{\cW}{\ensuremath{\mathcal{W}}}
\newcommand{\cX}{\ensuremath{\mathcal{X}}}
\newcommand{\cY}{\ensuremath{\mathcal{Y}}}
\newcommand{\cZ}{\ensuremath{\mathcal{Z}}}

% other useful shortcuts
\newcommand{\elementstack}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}
\newcommand{\8}{\infty}
\newcommand{\cond}{\text{cond}}
\newcommand{\argmin}[1]{\underset{#1}{\text{argmin}}}
\newcommand{\dx}{\text{ d}}
\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}
\newcommand{\Leftrightarrowequiv}{\overset{\cdot}{\Leftrightarrow}}
\newcommand{\Longleftrightarrowequiv}{\overset{\cdot}{\Longleftrightarrow}}
\newcommand{\Rightarrowequiv}{\overset{\cdot}{\Rightarrow}}
\newcommand{\Leftarrowequiv}{\overset{\cdot}{\Leftarrow}}
\newcommand{\defAs}{\overset{\text{def}}{=}}
\newcommand{\defEquiv}{\overset{\text{def}}{\Leftrightarrow}}
\newcommand{\defImplies}{\overset{\text{def}}{\Rightarrow}}
\newcommand{\diff}[1]{\frac{\mbox{d}}{\mbox{d}#1}}
\newcommand{\diffn}[2]{\frac{\mbox{d}^{#2}}{\mbox{d}^{#2}#1}}
\newcommand{\pardiff}[1]{\frac{\partial}{\partial #1}}
\newcommand{\pardiffn}[2]{\frac{\partial^{#2}}{\partial^{#2} #1}}
\newcommand{\divider}{\hspace{0.25em}|\hspace{0.25em}}
\newcommand{\lcm}{\text{lcm}}
\newcommand{\limit}[2]{\underset{#1 \rightarrow #2}{\lim}}
\newcommand{\limni}{\limit{n}{\infty}}
\newcommand{\limnz}{\limit{n}{0}}
\newcommand{\limxz}{\limit{x_0}{0}}
\newcommand{\limhz}{\limit{h}{0}}
\newcommand{\liminfni}{\liminf_{n \rightarrow \infty}}
\newcommand{\limsupni}{\limsup_{n \rightarrow \infty}}
\newcommand{\sequence}[1]{\ensuremath{(#1_n)_{n \geq 1}}}
\newcommand{\series}[2]{\ensuremath{\sum_{k = 1}^{#2} #1_k}}

\DeclareMathOperator\arctanh{arctanh}
\DeclareMathOperator\arccosh{arccosh}
\DeclareMathOperator\arcsinh{arcsinh}