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Variable Definition

In mathematics, a variable is a symbol used to represent an arbitrary element that can change or that may take on different values. Variables may also refer to a letter, symbol, or snippet of words or text, representing such a quantity. 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, or a basic object of the theory, which is manipulated without referring to its possible intuitive interpretation.