indeterminate

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, let's see two examples:

1. 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 $x$ .
2. 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.