Math & Science ⇒ Multiple exponents

[feynman44]

I'm having a few issues with the following expression:

bigexp.JPG (17.04 KiB) Viewed 12802 times

Code: Select all

\documentclass{article}
\usepackage{amsmath,mathdots}
\newcommand{\high}[1]{\text{\raisebox{0.6ex}{$#1$}}}
\newcommand{\higher}[1]{\text{\raisebox{1.5ex}{$#1$}}}

\begin{document}
\begin{equation*}
\left(2011^{{{2010}^{{\high{2009}}^{{\higher{\iddots}}^{{3^{\high{2}^\high{1}}}}}}}}\right)!
\end{equation*}
\end{document}

1) As you can see, I've defined a couple of commands in the preamble to help with the spacing, but I would rather have more accurate (automatic) spacing. I would also prefer to have all the numbers at the same font size, with the possible exception of 2011.

2) I want the lower edge of the parentheses to line up with the bottom of 2011, which obviously is not the case at the moment.

3) I would like the factorial symbol to be about as tall as the parentheses.

I am quite new to LaTeX so please be patient! If you have any other suggestions not mentioned above, I would be interested to hear those as well. :) Thanks in advance for your help!

[kaiserkarl13]

How about the following:

Code: Select all

\documentclass{article}
\usepackage{amsmath}
\begin{document}
  \begin{displaymath}
    \biggl( \raisebox{-0.8em}{$2011^{2010^{2009^{.^{.^{.^{3^{2^{1}}}}}}}}$} \big
  \end{displaymath}
\end{document}

If you really want the numbers to be the same size, try setting the size manually, like this:

Code: Select all

\documentclass{article}
\usepackage{amsmath}
\begin{document}
  \begin{displaymath}
    \biggl( \raisebox{-0.8em}{\text{\tiny 2011}$^{\text{\tiny 2010}^{2009^{.^{.^{.^{3^{2^{1}}}}}}}}$} \biggr)\raisebox{-0.5em}{\huge !}
  \end{displaymath}
\end{document}

I'm still wracking my brain trying to figure out why anyone would want to typeset such a construct, but that's not my business.

[feynman44]

Ah, that's much better - thank you! I invented this expression for a little problem-solving challenge...so nothing too practical, haha.