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They are all the same sort of thing on different levels of abstraction/generalization. Setting a value creates a more specialized (less general) version of the mathematical object (function, optimization problem, etc.), and replacing a formerly exactly defined value by a symbol creates a generalized problem (covering a whole family of the specific problems). ...


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A variable is, of course, a quantity that is allowed to vary over its range of definition. For example, $f(x) = 3x + 5$ is a function, where x ranges over the real numbers. Now, I think the difference between constants and parameters is a bit more subtle. First, constants: A constant is just something that doesn't vary. 3 is a constant value, $\pi$ is a ...


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A constant is something like a "number". It doesn't change as variables change. For example $3$ is a constant as is $\pi$. A parameter is a constant that defines a class of equations. $$\left(\frac xa\right)^2 + \left(\frac yb\right)^2 = 1$$ is the general equation for an ellipse. $a$ and $b$ are constants in this equation, but if we want to talk about ...



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