Cantor's diagonal argument

cantor.pdf

cantor.png

cantor.tex

\documentclass[crop]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usepackage{forloop}

\newcounter{n}
\setcounter{n}{10}	% change this value
\newcounter{j}
\newcounter{h}
\newcounter{x}
\newcounter{y}
\newcounter{xx}
\newcounter{yy}
\newcounter{nminusone}
\setcounter{nminusone}{-1}
\addtocounter{nminusone}{\value{n}}

\newcommand\tikzmark[2]{
	\tikz[remember picture,baseline] \node[inner sep=2pt,outer sep=0] (#1){#2};
}

\newcommand\link[2]{
	\begin{tikzpicture}[remember picture, overlay, >=stealth, shift={(0,0)}]
	\draw[->] (#1) to (#2);
	\end{tikzpicture}
}

\begin{document}
	\setlength{\tabcolsep}{.3em} % for the horizontal padding
	{\renewcommand{\arraystretch}{2}% for the vertical padding
			\begin{tabular}{*{\value{n}}{ c } }
				\forloop{y}{1}{\value{y} < \value{n}}
				{
					\forloop{x}{1}{\value{x} < \value{n}}
					{
						\ifnum\value{x}=\value{nminusone}
							\tikzmark{\they-\thex}{$...$} \uppercase{&}
						\else
							\ifnum\value{y}=\value{nminusone}
								\tikzmark{\they-\thex}{$...$} \uppercase{&}
							\else
								\tikzmark{\they-\thex}{$\frac{\they}{\thex}$} \uppercase{&}
							\fi
						\fi
					} 
					\\
				}
			\end{tabular}
	}
	\forloop{y}{1}{\value{y} < \value{n}}
	{
		\forloop{x}{1}{\value{x} <  \value{n}}
		{
			\setcounter{yy}{\value{y}}
			\setcounter{xx}{\value{x}}
			\newcount\h 
			\h=\value{n}\relax
			\advance\h-\value{y}
			\advance\h 1
			\ifnum\value{y}=1
				\ifcase\value{j}
					\addtocounter{yy}{1}
				\or
					\addtocounter{xx}{1}
				\or
					\addtocounter{yy}{1}
					\addtocounter{xx}{-1}
					\setcounter{j}{0}
				\fi
			\else
				\ifodd\value{y}
					\ifodd\value{x}
						\ifnum\value{x}=1
							\addtocounter{yy}{1}
							\ifnum\value{yy}=\value{n}
								\addtocounter{yy}{-1}
							\fi
						\else
							\ifnum\h>\value{x}
								\addtocounter{yy}{1}
								\addtocounter{xx}{-1}
							\fi
						\fi
					\else
						\ifnum\h>\value{x}
							\addtocounter{yy}{-1}
							\addtocounter{xx}{1}
						\fi
					\fi
				\else
					\ifodd\value{x}
						\ifnum\h>\value{x}
							\addtocounter{yy}{-1}
							\addtocounter{xx}{1}
						\fi
					\else
						\ifnum\h>\value{x}
							\addtocounter{yy}{1}
							\addtocounter{xx}{-1}
						\fi
					\fi
				\fi
			\fi
			\stepcounter{j}
			\advance\h -1
			\ifnum\h>\value{x}
				\link{\they-\thex}{\theyy-\thexx}
			\fi
		} 
	}	
\end{document}