# 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**.

## 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.

## Sources

- 1910: Alfred North Whitehead and Bertrand Russell:
*Principia Mathematica: Volume $\text { 1 }$*... (previous) ... (next): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations - 1972: Murray R. Spiegel and R.W. Boxer:
*Theory and Problems of Statistics*(SI ed.) ... (previous) ... (next): Chapter $1$: Discrete and Continuous Variables - 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 3$: Statements and conditions; quantifiers - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**range**:**2.** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**variable**:**1.** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**range**:**2.** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**variable**:**1.**