In mathematics, a **variable** is a symbol which functions as a placeholder for varying expression or quantities, and is often used to represent an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions.^{[1]}^{[2]}

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.

In calculus and its application to physics and other sciences, it is rather common to consider a variable, say *y*, whose possible values depend on the value of another variable, say *x*. In mathematical terms, the *dependent* variable *y* represents the value of a function of *x*. To simplify formulas, it is often useful to use the same symbol for the dependent variable *y* and the function mapping *x* onto *y*. For example, the state of a physical system depends on measurable quantities such as the pressure, the temperature, the spatial position, ..., and all these quantities vary when the system evolves, that is, they are function of the time. In the formulas describing the system, these quantities are represented by variables which are dependent on the time, and thus considered implicitly as functions of the time.

Therefore, in a formula, a **d**

**In calculus and its application to physics and other sciences, it is rather common to consider a variable, say y, whose possible values depend on the value of another variable, say x. In mathematical terms, the dependent variable y represents the value of a function of x. To simplify formulas, it is often useful to use the same symbol for the dependent variable y and the function mapping x onto y. For example, the state of a physical system depends on measurable quantities such as the pressure, the temperature, the spatial position, ..., and all these quantities vary when the system evolves, that is, they are function of the time. In the formulas describing the system, these quantities are represented by variables which are dependent on the time, and thus considered implicitly as functions of the time.
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**Therefore, in a formula, a dependent variable is a variable that is implicitly a function of another (or several other) variables. An independent variable is a variable that is not dependent.^{[7]}
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**The property of a variable to be dependent or independent depends often of the point of view and is not intrinsic. For example, in the notation f(x, y, z), the three variables may be all independent and the notation represents a function of three variab**

**Therefore, in a formula, a dependent variable is a variable that is implicitly a function of another (or several other) variables. An independent variable is a variable that is not dependent.^{[7]}
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**The property of a variable to be dependent or independent depends often of the point of view and is not intrinsic. For example, in the notation f(x, y, z), the three variables may be all independent and the notation represents a function of three variables. On the other hand, if y and z depend on x (are dependent variables) then the notation represents a function of the single independent variable x.^{[8]}
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**If one defines a function f from the real numbers to the real numbers by
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