Variable (mathematics)

Article summary

In mathematics, a variable (from Latin ) is a symbol, typically a letter, that refers to an unspecified mathematical object. One says colloquially that the variable represents or denotes the object, and that any valid candidate for the object is the value of the variable. The values a variable can take are usually of the same kind, often numbers. More specifically, the values involved may form a set, such as the set of real numbers. The object may not always exist, or it might be uncertain whether any valid candidate exists or not. For example, one could represent two integers by the variables and and require that the value of the square of is twice the square of , which in algebraic notation can be written . A definitive proof that this relationship is impossible to satisfy when and are restricted to nonzero integers isn't obvious, but it has been known since ancient times and has had a big influence on mathematics ever since. Originally, the term variable was used primarily for the argument of a function, in which case its value could be thought of as varying within the domain of the function. This is the motivation for the choice of the term. Also, variables are used for denoting values of functions, such as the symbol in the equation , where is the argument and denotes the function itself.…

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