In the present work is contrasted the metric conceptualization of limit, given by Weierstrass, that is utilized traditionally in the teaching, with its conceptualization as optimum approximation, given by Blázquez and Ortega (2002), to establish which of the two is simpler and appropriate for the initial teaching-learning of such notion. It is described the analysis of the data provided by two exploration works and, finally, its conclusions are enunciated, corroborating that the second conceptualization is simpler than the first one and, therefore, the most appropriate for the initial learning.
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