indeterminateIndeterminate2004-11-04 12:45:562004-11-04 15:51:11Definition% 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,amscd}
\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\PMlinkescapeword{solvable}
\PMlinkescapeword{alphabet}
An {\em indeterminate}\, is simply a variable that is not known or solvable. \,It is usually denoted by a mathematical alphabet ($x$, $y$, $z$, or $\alpha$, $\beta$, etc...). \,It is important to distinguish between a variable and an indeterminate in that a variable is solvable, at least conditionally. \,To make this more precise, let's see two examples:
\begin{enumerate}
\item Let $x$ be a variable such that \,$2+3x=a+bx$, where $a,b\in\mathbb{Q}$. Then \,$x=(a-2)/(3-b)$. \,Here $x$ is solvable conditioned on the equation given. Any values of $a$ and $b\,(\neq 3)$ will yield a value for $x$.
\item Let $x$ be an indeterminate such that \,$2+3x=a+bx$, where \,$a,\,b\in\mathbb{Q}$. \,Since $x$ can not be solved, we have \,$2=a$\, and \,$3=b$. \,Note that if $a$ and $b$ are previously assigned to be values other than 2 and 3 respectively, then $x$ is no longer an indeterminate.
\end{enumerate}