additive basis Basis2 2002-12-26 04:12:32 2002-12-26 18:16:33 Definition order of additive basis % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here A subset $A$ of $\mathbb{Z}$ is an \emph{(\PMlinkescapetext{additive}) basis} of \PMlinkescapetext{order} $n$ if \begin{equation*} nA=\mathbb{N}\cup\{0\}, \end{equation*} where $nA$ is $n$-fold sumset of $A$. Usually it is assumed that $0$ belongs to $A$ when saying that $A$ is an additive basis.