## ::Variable (mathematics)

### ::concepts

Function::variable ''x''::which Constant::often ''y''::number Called::''f'' Example::''a''

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In elementary mathematics, a **variable** is an alphabetic character representing a number, called the **value** of the variable, which is either arbitrary or not fully specified or unknown. 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 to the variables that represent them.

The concept of **variable** is also fundamental in calculus.
Typically, a function *y* = *f*(*x*) involves two variables, *y* and *x*, representing respectively the value and the argument of the function. The term "variable" comes from the fact that, when the argument (also called the "variable of the function") *varies*, then the value *varies* accordingly.<ref>{{#invoke:citation/CS1|citation
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In more advanced mathematics, a **variable** is a symbol that denotes a mathematical object, which could be a number, a vector, a matrix, or even a function. In this case, the original property of "variability" of a variable is not kept (except, sometimes, for informal explanations).

Similarly, in computer science, a **variable** is a name (commonly an alphabetic character or a word) representing some value represented in computer memory. 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.

**Variable (mathematics) sections**

Intro Etymology Genesis and evolution of the concept Specific kinds of variables Notation See also Bibliography References

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