The ideas, results and reflections that we develop, are product of studies and part of investigations (Garbin 2000, 2003, 2005 and Garbin & Azcárate, 2001) that have intended to contribute with the debate of the problems of the mathematical infinite in their potentialactual duality (Fischbein, Tirosh & Hess (1979), Sierspinska (1987), Tall (1980), Tirosh, (1991), Moreno & Waldegg (1991), Tsamir & Tirosh, (1994), D’ Amore (1997), Tall (2001), Fischbein, 2001) that generates the influence of the representations and different mathematical languages on the perceptions of the infinite and mathematical reasoning associates, and in the weaknesses and inconsistencies of the student’s answers to problems in which infinite processes are present.
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