AN EPISTEMOLOGICAL ANALYSIS OF THE FORMULATION OF WEIERSTRASS’ LIMIT DEFINITION OF A FUNCTION AT A POINT
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Abstract
This paper presents an epistemological analysis that clarifies the process of forming the Weierstrass' epsilon-delta limit definition of functions. The study analyzes the origin of the concept of limit and the conditions for forming the Weierstrass limit definition of functions over the periods from Antiquity to the end of the 19th century. The research results allow determining two mathematical perspectives that influenced the formulation of Weierstrass' definition, rigorization and arithmetization of analysis; and the epistemological obstacles associated with Weierstrass' definition. The research results contribute to clarifying the epistemological origin of the difficulties and mistakes encountered by preservice students of Mathematics when approaching the Weierstrass' epsilon-delta limit definition of functions.
Keywords
arithmetization, epistemological analysis, epsilon-delta, obstacle, limit of function, rigorization
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