\documentclass[]{article} \usepackage{amsmath} \usepackage{tikz} \usepackage{listings} \usepackage{pagecolor} \usepackage{xcolor} \color{green} \newcommand{\HO}[1]{% \begin{tikzpicture}[#1]% \draw (0,1.3ex) -- (3ex,1.3ex);% \draw (1.5ex,1ex) -- (1.5ex,1.6ex);% \end{tikzpicture}% } \newcommand{\IHO}[1]{% \begin{tikzpicture}[#1]% \draw (0,0.2ex) -- (3ex,0.2ex);% \draw [line width=0.6mm] (1.5ex,0.001ex) -- (1.5ex,0.08ex);% \end{tikzpicture}% } \begin{document} \pagecolor{black} \section{Notation} \subsection{Hyperoperation} $$a+b = a {\overset{1}{\HO{scale=2}}} b$$ $$a \cdot b = a {\overset{2}{\HO{scale=2}}} b$$ $$a ^{b} = a {\overset{3}{\HO{scale=2}}} b$$ $$\label{hyperoperator} \underbrace{a {\overset{n}{\HO{scale=2}}} a {\overset{n}{\HO{scale=2}}} … a}_\text{b} = a {\overset{n+1}{\HO{scale=2}}} b$$ \subsection{Inverse-hyperoperation} $$c \overset{1}{\IHO{scale=2}} b =c-b$$ $$c \overset{2}{\IHO{scale=2}} b =\frac{c}{b}$$ $$c \overset{3}{\IHO{scale=2}} b =\log_{b} c$$ $$\label{hyperoperator} c {\overset{n}{\IHO{scale=2}}} b = a$$ \subsection{Hyperoperations with fractional "exponents"} $$a+\frac{b}{q} = a {\overset{1}{\HO{scale=2}}} \frac{b}{q}$$ $$a \cdot \frac{b}{q} = a {\overset{2}{\HO{scale=2}}} \frac{b}{q}$$ $$a ^{\frac{b}{q}} = \sqrt[q]{a^{b}} = a {\overset{3}{\HO{scale=2}}} \frac{b}{q}$$ $$\label{hyperoperator} \underbrace{a {\overset{n}{\HO{scale=2}}} a {\overset{n}{\HO{scale=2}}} … a}_\text{"b/q"} = a {\overset{n+1}{\HO{scale=2}}} \frac{b}{q}$$ \end{document}