L’HÔPITAL BLINDNESS IN EXCEL: THE COMPUTATIONAL COLLAPSE BETWEEN INDETERMINACY (0/0) AND UNDEFINED DIVISION (A/0) AND ITS IMPLICATIONS FOR GLOBAL MATHEMATICS EDUCATION
Abstract
The distinction between indeterminacy and impossibility constitutes a fundamental principle of mathematics. While 0/0 represents an indeterminate form, the division of a nonzero number by zero is not defined within the set of real numbers. Although this distinction is well established in calculus, its representation in digital tools may take divergent forms. This study investigates this phenomenon through a comparative experimental analysis across four contexts: calculations performed in spreadsheet cells and VBA routines in Microsoft Excel, results produced by the Windows Calculator, and conceptual interpretations provided by an artificial intelligence system. The results show that, in Excel’s cell environment, mathematically distinct expressions are reduced to a single error condition, characterizing a computational collapse in the representation of these operations. In contrast, both the VBA environment and the operating system calculator, as well as the conceptual interpretation analyzed, preserve the distinction between the cases considered. These findings demonstrate that different computational environments may treat fundamental mathematical operations in non-equivalent ways, with relevant implications for educational contexts. By obscuring essential conceptual distinctions, certain representations may influence the understanding of basic notions of mathematical analysis, particularly in technology-mediated learning situations.
Author Biography
Escritor e professor universitário em temas relacionados às ciências exatas e tecnologias educacionais. Mestre em Ciências Naturais e Matemática pela Universidade Regional de Blumenau – FURB (2012). Especialista em Metodologia do Ensino de Matemática pelo IBPEX (2006). Bacharel em Ciências Contábeis pela Universidade da Região de Joinville – UNIVILLE (2000). Possui formação pedagógica de docentes pelo Centro Universitário de Jaraguá do Sul – UNERJ (2006). Atua como professor no ensino profissional e tecnológico, nas modalidades de ensino técnico de nível médio, graduação tecnológica e pós-graduação. Possui mais de 20 anos de experiência em processos contábeis, administrativos e produtivos na região do Vale do Itapocu – SC.
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