Function (mathematics)
In 1748, Leonhard Euler gave the following definition for function:"A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities."and then in 1755:"If some quantities so depend on other quantities that if the latter are changed the former undergoes change, then the former quantities are called functions of the latter. This definition applies rather widely and includes all ways in which one quantity could be determined by other. If, therefore, x denotes a variable quantity, then all quantities which depend upon x in any way, or are determined by it, are called functions of x."Usually, Peter Dirichlet is credited with the first modern definition of function (formulated in 1837). It is often used in schools until the second half of the 20th century:"y is a function of a variable x, defined on the interval a < x < b, if to every value of the variable x in this interval there corresponds a definite value of the variable y. Also, it is irrelevant in what way this correspondence is established."In 1939, the Bourbaki generalized the Dirichlet definition, and gave a set-theoretic version of the definition as a correspondence between inputs and outputs; this was used in schools from about 1960.