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As a mathematical term, "'''function'''" was coined by [[Gottfried Leibniz|Leibniz]] in [[1694]], to describe a quantity related to a [[curve]], such as a curve's [[slope]] or a specific [[point]] of a curve. The functions Leibniz considered are today called [[derivative|differentiable functions]], and they are the type of function most frequently encountered by nonmathematicians. For this type of function, one can talk about [[limit of a function|limit]]s and [[derivative]]s; both are measurements of the change of output values associated to a change of input values, and these measurements are the basis of [[calculus]].
The word function was later used by [[Leonhard Euler|Euler]] during the mid-[[18th Century]] to describe an [[expression]] or formula involving various [[parameter|argument]]s, e.g. ''f''(''x'') = sin(''x'') + ''x''<sup>3</sup>.
During the [[19th Century]], mathematicians started to formalize all the different branches of mathematics. [[Karl Weierstrass|Weierstrass]] advocated building calculus on [[arithmetic]] rather than on [[geometry]], which favoured Euler's definition over Leibniz's (see [[arithmetization of analysis]]).
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