The relation between integer sequences and set theory

In my work, sequences of integers and their relation to set theory were examined. It was noticed in the literature review that the generalization of the solutions of some problems in set theory was not given, and it was tried to find solutions to these problems. In the subject of clusters, the relations of the subset elements with each other were examined. The problems were examined by blending the subject of arrays with the subject of sets. General solutions to the problems were produced by producing four different formulas. During the production stages of the solutions, the Fibonacci rabbit diagram was handled from a different perspective. Working with tables, charts and diagrams was supported. In the first chapter, Fibonacci, Lucas, Cassini and integer sequences were mentioned. Relationships with each other were examined. In the second part of my work, set theory and how my work can find a solution to a problem in the aviation industry were mentioned. In the third part of my work, two different problems in set theory were generalized and solutions were obtained. While obtaining the solutions, the relationship with the integer sequences was revealed. In the fourth chapter, information was given about how the problems can be analyzed in different dimensions and how they can be used in new studies. In addition, a new problem that emerged from the solution of the problem was mentioned. The contributions of my work were mentioned when solving the new problem in the future.