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The mathematical concept of a function (and the name) emerged in the 17th century in connection with the development of the calculus; for example, the slope ''dy/dx'' of a graph at a point was regarded as a function of the ''x''-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as Oresme. Mathematicians of the 18th century typically regarded a function as being defined by an analytic expression. In the 19th century, the demands of the rigorous development of analysis by Weierstrass and others, the reformulation of geometry in terms of analysis, and the invention of set theory by Cantor, eventually led to the much more general modern concept of a function as a single-valued mapping from one set to another. ==Functions before the 17th century== According to Dieudonné and Ponte,〔"The emergence of a notion of function as an individualized mathematical entity can be traced to the beginnings of infinitesimal calculus". ()〕 the concept of a function emerged in the 17th century as a result of the development of analytic geometry and the infinitesimal calculus. Nevertheless, Medvedev suggests that the implicit concept of a function is one with an ancient lineage.〔"...although we do not find in (mathematicians of Ancient Greece ) the idea of functional dependence distinguished in explicit form as a comparatively independent object of study, nevertheless one cannot help noticing the large stock of functional correspondences they studied." ()〕 Ponte also sees more explicit approaches to the concept in the Middle Ages: :Historically, some mathematicians can be regarded as having foreseen and come close to a modern formulation of the concept of function. Among them is Oresme (1323–1382) . . . In his theory, some general ideas about independent and dependent variable quantities seem to be present. The development of analytical geometry around 1640 allowed mathematicians to go between geometric problems about curves and algebraic relations between "variable coordintaes ''x'' and ''y''." Calculus was developed using the notion of variables, with their associated geometric meaning, which persisted well into the eighteenth century. However, the terminology of "function" came to be used in interactions between Leibniz and Bernoulli towards the end of the 17th century. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「History of the function concept」の詳細全文を読む スポンサード リンク
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