# Definition:Variable/Domain

## Definition

The collection of all possible objects that a variable may refer to has to be specified.

This collection is the domain of the variable.

## Also known as

The domain of a variable is sometimes referred to imprecisely as the values of the variable, or its range of values.

In the context of real functions, the domain is sometimes seen as the interval of definition.

## Examples

### Litres of Water in Washing Machine

Let $V$ be the number of litres of water in a washing machine.

The domain of $V$ is the closed interval $\closedint 0 C$, where $C$ is the capacity of the washing machine.

$V$ is a continuous variable.

### Books on Library Shelf

Let $B$ be the number of books on a library shelf.

The domain of $B$ is the closed interval $\closedint 0 C$, where $C$ is the largest number of books that can be held on a shelf.

$B$ is a discrete variable.

### Points on Pair of Dice

Let $S$ be the total number of points that are obtained when tossing a pair of dice.

The domain of $S$ is the set $\set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}$.

$S$ is a discrete variable.

### Diameter of Sphere

Let $d$ be the diameter of a sphere.

The domain of $d$ is the open interval $\openint 0 \to$.

$d$ is a continuous variable.

### Countries in Europe

Let $C$ be a country in Europe.

The domain of $C$ is the set $\set {\text {France}, \text {Germany}, \text {Spain}, \text {Italy}, \ldots}$

These can be represented numerically if desired, by assigning an integer to each of the countries in Europe, for example:

$1: \text {France}$
$2: \text {Germany}$
$3: \text {Spain}$
$4: \text {Italy}$
$\vdots$

$C$ is a discrete variable.