# Definition:Independent Variable

## 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 $x$.