Indeterminate (variable)

An 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, compare the two situations below.

1. Let $x$ be a variable such that

$2+3x=a+bx$,

where $a$ and $b$ are in the rationals 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 $x$.

2. Let $x$ be an indeterminate such that

$2+3x=a+bx$,

where $a$ and $b$ are again in Q. Since $x$ can not be solved for, 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.

See also

• Polynomial

indeterminate at PlanetMath.