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indeterminate (Definition)

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.



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Cross-references: equation, variable
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This is version 2 of indeterminate, born on 2004-11-04, modified 2004-11-04.
Object id is 6444, canonical name is Indeterminate.
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Classification:
AMS MSC00A05 (General :: General and miscellaneous specific topics :: General mathematics)

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