The big O, big theta, and other notations form the family of Bachmann-Landau or asymptotic notations. These notations describe the limiting behavior of a function in mathematics or classify algorithms in computer science according to their complexity / processing time. In this post, I’m not so much interested in the definition of these notations, but rather in how to correctly typeset them in LaTeX.
Example of a big O notation
There are two possible ways to type the big O:
1 2 3 | $O(n\log{}n)$ % regular O$\mathcal{O}(n\log{}n)$ % Open at top left |
The latter produces the following:
No additional package is required for either of these.
Complete list of Bachmann-Landau notations
The complete list of Bachmann-Landau or asymptotic notations is given below. To copy-paste any of these, use the source code.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | \documentclass[11pt]{article}\newcommand{\bslash}{\char`\\}\begin{document}\section*{Big O notations}$\mathcal{O}(n\log{}n)$\section*{Family of Bachmann-Landau notations}\setlength{\tabcolsep}{12pt}\renewcommand*{\arraystretch}{1.2}\begin{tabular}{lcl}\hlineName&Notation&Command\\\hline{\bf Big O(micron)}&$\mathcal{O}$ or $O$&\texttt{\$\bslash mathcal\{O\}\$ or \$O\$}\\{\bf Big Omega}&$\Omega$&\texttt{\$\bslash Omega\$}\\{\bf Big Theta}&$\Theta$&\texttt{\$\bslash Theta\$}\\{\bf Small O(micron)}&$o$&\texttt{\$o\$}\\{\bf Small Omega}&$\omega$&\texttt{\$\bslash omega\$}\\{\bf On the order of}&$\sim$&\texttt{\$\bslash sim\$}\\\hline\end{tabular}\end{document} |
Very nice!
Thank you for that small tip. Just thought about investing an hour how to write this down properly.
This may be usefull:
\renewcommand{\O}[1]{$\mathcal{O}(#1)$}Thanks, interesting suggestion! Here is a minimal working example for illustration:
\documentclass[11pt]{article}\renewcommand{\O}[1]{$\mathcal{O}(#1)$}\begin{document}\O{n}\end{document}It is very nice, but I would define a new command so that the original meaning of `
\O` (which gives us Ø) is not lost. So I would do like this\newcommand\bigO[1]{$\mathcal{O}(#1)$}A good point, thanks much. Best, Tom
thank you