A variable is a non-numerical symbol used in a mathematical expression that serves as a placeholder for any of a specified set of values. A large part of elementary algebra is devoted to learning techniques for determining the value (or set of possible values) of a variable that appears in an equation or inequality.
In theory, any symbol (other than a number) can be used to represent a variable. In practice, letters (usually English or Greek) are used as they make communication easier.
There are some symbols that are rarely used as variables because they are by convention treated as the names of specific constants. They include:
- e — typically representative of Euler's number.
- π — pi, which has multiple mathematical meanings but is most commonly used to represent the ratio of a circle's circumference to its diameter (approximately 3.14159).
- o — usually avoided by mathematicians for risk of confusion with the empty set (∅) or the numeral zero (0). (But see Order notation, Big O notation and Little O notation.)
Other symbols are often treated as the names of functions or other mathematical objects and so make poor choices of variable names. For example:
- f — the prototypical name of a function.