Definition:Independent Variable

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Definition

Real Function

Let $f: \R \to \R$ be a real function.

Let $f \left({x}\right) = y$.

Then $x$ is referred to as an independent variable.


Complex Function

Let $f: \C \to \C$ be a complex function.

Let $\map f z = w$.


Then $z$ is referred to as an independent variable (of $f$).


Also see

The terms independent variable and dependent variable arise from the idea that it is usual to consider that $x$ can be chosen independently of $y$, but having chosen $x$, the value of $y$ then depends on the value of $x$.