A cognitive approach for understanding the comparison between the cardinals of the set of natural numbers and the set of integers in secondary student

Abstract

This research studies the mental structures and mechanisms of 164 Chilean students of third and fourth half (17 and 18 years old), when comparing the cardinal of the set of natural numbers (ℕ) and the cardinal of integers (ℤ). It is based on a provisional genetic decomposition of infinity within the framework of APOS theory, and shows that students establish only an injective function from ℕ to ℤ to coordinate the infinite iterative processes and, furthermore, they do not manage to present the structure of a single infinite iterative process that would allow them to conclude that they have the same cardinal number.