JOURNAL OF DIALECTICS OF NATURE
A Comprehensive, Academic Journal of the Philosophy, History, Sociology and Cultural Studies of Science and Technology
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LI Yaya
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Research Articles
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The Historical Development of the Concept of Function’s Continuity: From Euler to Lebesgue Abstract: The function is a basic concept in mathematics, and continuity is one of its important properties. The concept of a function’s continuity stems from geometric intuition. Because a function was defined as analytical expressions, a continuous function was initially seen as one determined by a single analytical law. Following the trend towards rigor in analysis, Cauchy gave the concept of a function’s continuity in the modern sense by formulating the geometric notion of continuity. Based on Cauchy’s work, Weierstrass gave the current definition of a function’s continuity. The historical exploration on the evolution of the concept of a function’s continuity can provide a window into the rigorous process of analysis. Key Words: Rigor in analysis; Function; Continuity; Differentiability; IntegrabilityIssue:Volume 46, lssue 2, February 2024Page: 61-67
JOURNAL OF DIALECTICS OF NATURE
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