Variable (mathematics)

In mathematics, a variable is a symbol which works as a placeholder for expression or quantities that may varyor change; is often used to represent the argument of a function or an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions.

Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation—by simply substituting the numeric values of the coefficients of the given equation for the variables that represent them.

In mathematical logic, a variable is either a symbol representing an unspecified term of the theory (i.e., meta-variable), or a basic object of the theory—which is manipulated without referring to its possible intuitive interpretation.