The Problem of the Irregular Element and its Implications for SDG 4 – Quality Education

Introduction: In a set of identical elements (regular elements) is inserted another element (irregular element) which in all observable characteristics has the same as those of regular elements but, according to an unobservable feature, he differs from them. So we obtain a set S with n elements. The irregular element can have positive or negative deviation of a specific feature compared to the regular elements of the set S. A characteristic of the feature of the irregular element is that its presence in any subset A of S gives it a deviation compared with any subset B with the same number of elements, but that all its elements are regular. Of course, this deviation has the direction of the set that contains the irregular element. Supposed that a comparison operation is available, for each pair of subsets of S with the same number of elements, to indicates whether or not one of them has a positive deviation from the other, which means that the irregular element belongs to one of these two sets, but without knowing which of them. Under these conditions, it is clear that with at most comparison operations between two subsets with one element each, it is possible to identify the irregular element. But, the problem we will pose here is that of identifying this element with as few comparison operations as possible between the subsets of S, where S is a set with n elements. Objective: The objective of this study is that of identifying this irregular element with as few comparison operations as possible between the subsets of S. Theoretical Framework: In this topic, the main concepts and theories that underpin the research are presented. The most impotant one is the set theori and combinatorics. Method: In this paper we have adopted a procedure of comparison operations between the subsets of S as mentioned above. Results and Discussion: The results obtained here show an another way of operating to identify the irregular element in the set of elements. Originality/Value: This is an originality study and we think it contributes to the literature to find the shortest way to resolve the known problem of the irregular element in a set of elements.