3

I would like to produce an illustration for Cantor's diagonal argument, something like a centered enumeration of $4$ or $5$ decimal expansions $x_{i} = .d_{i1}d_{i2}d_{i3} \ldots$, and then insert a diagonal oval circumscribing $d_{11}, d_{22}, d_{33}, \ldots$.

What is a good way to do this?

I have come up with the following, but I'm not sure it will allow me to insert the diagonal oval? (which I don't know how to do.)

Any constructive comments are appreciated.

I don't know if the latex documentation will format properly as this is my first question post on this site.

Thank you.

\documentclass{book} \usepackage{amsthm,latexsym,amssymb,amsmath,verbatim}

\pagestyle{empty}

\begin{document}

[ x_{1} = .d_{11}d_{12}d_{13}d_{14}d_{15} \ldots ] [ x_{2} = .d_{21}d_{22}d_{23}d_{24}d_{25} \ldots ] [ x_{3} = .d_{31}d_{32}d_{33}d_{34}d_{35} \ldots ] [ x_{4} = .d_{41}d_{42}d_{43}d_{44}d_{45} \ldots ] [ x_{5} = .d_{51}d_{52}d_{53}d_{54}d_{55} \ldots ] [ \hskip -100pt \vdots ]

\end{document}
  • 1
    MathJax isn't enabled on this site, so math expressions aren't rendered as math. To highlight code properly, select it and hit Ctrl + K (or click the button marked {} above the input field). – Torbjørn T. Jul 27 at 18:35
  • Thank you, I did not know that. (And thank you for your edit.) – mlchristians Jul 27 at 18:36
7

I propose this code, based on alignat and pstricks:

\documentclass[11pt, svgnames]{book}

\usepackage{amsthm,latexsym,amssymb,amsmath, verbatim}
\usepackage{makebox}
\usepackage{pst-node, auto-pst-pdf}
\pagestyle{empty}

\begin{document}

\begin{postscript}
\everypsbox{\scriptstyle}
\begin{alignat*}{7}
 x_{1} & = . &\: & d_{\rnode{d1}{1}1} & & d_{12} & & d_{13} & & d_{14} & & d_{15} & \; & \ldots \\
 x_{2} & = . & & d_{21} & \enspace & d_{\rnode{d2}{2}2} & & d_{23} & & d_{24} & & d_{25} & & \ldots \\
 x_{3} & = . & & d_{31} & & d_{32} & \enspace & d_{ \rnode{d3}{3}3} & & d_{34} & & d_{35} & & \ldots \\
 x_{4} & = . & & d_{41} & & d_{42} & & d_{43} & \enspace & d_{\rnode{d4}{4}4} & & d_{45} & & \ldots \\
 x_{5} & = . & & d_{51} & & d_{52} & & d_{53} & & d_{54} & \enspace & d_{\rnode{d5}{5}5} & & \ldots\\[-1.33ex]
 \makebox*{$x_{5}$}{$ \vdots $} & & & & & & & \makebox*{$d_{53}$}{$ \vdots $} & & & & & \enspace & \Rnode{dd}{\ddots}
\end{alignat*}
\ncbox[boxsize=0.22, linearc=0.22, linecolor=FireBrick, nodesep=1.5ex, fillstyle=solid, fillcolor=FireBrick!20, opacity=0.3]{d1}{dd}
 \end{postscript}

\end{document}

enter image description here

  • This is much nicer than I had hoped for! Thank you. – mlchristians Jul 27 at 21:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.