Definition:Independent Variable

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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 known as

An independent variable can also be referred to as an argument.

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 $x$.