Variable (mathematics)

In mathematics, a variable (from Latin variabilis, "changeable") is a symbol and placeholder for (historically) a quantity that may change, or (nowadays) any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.[1]

Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves every quadratic equation by 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 (a meta-variable), or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation.

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