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Viewing Version
8
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'difference'
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| Title of object: |
difference |
| Canonical Name: |
Difference2 |
| Type: |
Definition |
| Created on: |
2007-09-27 09:15:56 |
| Modified on: |
2008-02-09 13:36:09 |
| Classification: |
msc:11B25, msc:00A05, msc:20K99 |
| Defines: |
minuend, subtrahend |
Preamble:
% 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
\theoremstyle{definition}
\newtheorem*{thmplain}{Theorem}
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Content:
The {\em difference} of two numbers $a$ and $b$ is a number $d$ such that
$$b\!+\!d = a.$$
The difference of $a$ (the {\em minuend}) and $b$ (the {\em subtrahend}) is denoted by $a\!-\!b$.
The definition is \PMlinkescapetext{similar} for the elements $a,\,b$ of any \PMlinkescapetext{additive} Abelian group (e.g. of a vector space).\,The difference of them is always unique.\\
\textbf{Some \PMlinkescapetext{identities}}
\begin{itemize}
\item $b\!+\!(a\!-\!b) = a$
\item $a\!-\!b = a\!+\!(-b)$
\item $-(a\!-\!b) = b\!-\!a$
\item $n(a\!-\!b) = na\!-\!nb \quad (n\in\mathbb{Z})$
\end{itemize}
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