A **variable** is something which is subject to change; the term is most commonly used in computer science and mathematics, where it denotes a quantity or symbolic representation (one which is often unknown).

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2 Why Are Variables Useful? 3 Computer Science |

## General Overview

Variables are used in open sentences. For instance, in the formula:**x**+ 1 = 5,

**x**is a variable which represents an "unknown" number. In mathematics, variables are usually represented by letters of the Roman alphabet, but are also represented by letters of other alphabets; as well as various other symbols. In computer programming, variables are usually represented by either single letters or alphanumeric stringss.

## Why Are Variables Useful?

Variables are useful in mathematics and computer programming because they allow instructions to be specified in a general way. If one were forced to use actual values, then the instructions would only apply in a more narrow, and specific, set of situations. For example: specify a mathematical definition for finding the square of ANY number: square(**x**) =

**x***

**x**.

Now, all we need to do to find the square of a number is replace **x** with any number we want.

- square(x) = x * x = y
- square(1) = 1 * 1 = 1
- square(2) = 2 * 2 = 4
- square(3) = 3 * 3 = 9

In the above example, the variable **x** is a "placeholder" for ANY number. One important thing we are assuming is that the value of each occurrence of **x** is the same -- that **x** does not get a new value between the first **x** and the second **x**.
In computer programming languages without referential transparency, such changes can occur.