diff --git a/main/math.tex b/main/math.tex
index 63da9a4..1c04894 100644
--- a/main/math.tex
+++ b/main/math.tex
@@ -8,14 +8,47 @@
 % ▄███▄ ▀▀  ▄████▄████▀██▄ ▀███████  ████▄
 
 
-\newcommand{\R}{\mathbb{R}}
-\newcommand{\N}{\mathbb{N}}
+% BB shortcuts (for number spaces, etc)
 \newcommand{\C}{\mathbb{C}}
-\newcommand{\Q}{\mathbb{Q}}
-\newcommand{\Z}{\mathbb{Z}}
-\newcommand{\I}{\mathbb{I}}
-\newcommand{\E}{\mathbb{E}}
 \newcommand{\D}{\mathbb{D}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\I}{\mathbb{I}}
+\newcommand{\J}{\mathbb{J}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\Q}{\mathbb{Q}}
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\V}{\mathbb{V}}
+\newcommand{\Z}{\mathbb{Z}}
+
+% Caligraphic
+\newcommand{\cA}{\mathcal{A}}
+\newcommand{\cB}{\mathcal{B}}
+\newcommand{\cC}{\mathcal{C}}
+\newcommand{\cD}{\mathcal{D}}
+\newcommand{\cE}{\mathcal{E}}
+\newcommand{\cF}{\mathcal{F}}
+\newcommand{\cG}{\mathcal{G}}
+\newcommand{\cH}{\mathcal{H}}
+\newcommand{\cI}{\mathcal{I}}
+\newcommand{\cJ}{\mathcal{J}}
+\newcommand{\cK}{\mathcal{K}}
+\newcommand{\cL}{\mathcal{L}}
+\newcommand{\cM}{\mathcal{M}}
+\newcommand{\cN}{\mathcal{N}}
+\newcommand{\cO}{\mathcal{O}}
+\newcommand{\cP}{\mathcal{P}}
+\newcommand{\cQ}{\mathcal{Q}}
+\newcommand{\cR}{\mathcal{R}}
+\newcommand{\cS}{\mathcal{S}}
+\newcommand{\cT}{\mathcal{T}}
+\newcommand{\cU}{\mathcal{U}}
+\newcommand{\cV}{\mathcal{V}}
+\newcommand{\cW}{\mathcal{W}}
+\newcommand{\cX}{\mathcal{X}}
+\newcommand{\cY}{\mathcal{Y}}
+\newcommand{\cZ}{\mathcal{Z}}
+
+% other useful shortcuts
 \newcommand{\8}{\infty}
 \newcommand{\dx}{\text{ d}}
 \newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}
@@ -39,6 +72,9 @@
 \newcommand{\seq}[1]{(#1_n)_{n \geq 1}}
 \newcommand{\ser}[2]{\sum_{k = 1}^{#2} #1_k}
 \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{\elementstack}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}