# Definition:Independent Variable

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## Definition

### Real Function

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

Let $\map f x = y$.

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 $x$.

## Sources

- 1972: Murray R. Spiegel and R.W. Boxer:
*Theory and Problems of Statistics*(SI ed.) ... (previous) ... (next): Chapter $1$: Functions - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**argument**:**3.**