What It Means For A Variable To Vary
Varying, in the context of mathematical variables, does not mean change in the course of time, but rather dependence on the context in which the variable is used. This can be the immediate context of the expression in which the variable occurs, as in the case of summation variables or variables that designate the argument of a function being defined. The context can also be larger, for instance when a variable is used to designate a value occurring in a hypothesis of the discussion at hand. In some cases nothing varies at all, and alternative names can be used instead of "variable": a parameter is a value that is fixed in the statement of the problem being studied (although its value may not be explicitly known), an unknown is a variable that is introduced to stand for a constant value that is not initially known, but which may become known by solving some equation(s) for it, and an indeterminate is a symbol that need not stand for anything else but is an abstract value in itself. In all these cases the term "variable" is often still used because the rules for the manipulation of these symbols are the same.
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