On introducing a set perspective in the learning of limits of real sequences

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that arises provides students with an alternative source for proving propositions concerning limiting properties of sequences. Some examples are given and comments are made on the cognitive level.

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