An approach to simulate basic concepts of mathematics with object-oriented programming

Abstract

Traditional approaches to using data structures mainly focus on the improvement in algorithm efficiency but rarely take advantage of object-oriented programming that can simulate the definition of mathematic concepts in a way that is similar to human thinking mode, so traditional approaches cannot satisfy the need of simulating sets and their features and operations for mathematics studies. In this paper, the author pointed out the disadvantages of traditional ways, proposed a series of hypotheses describing the relationship between sets and classes such as inheriting and inclusion relationships and a way based on those hypotheses using features of object-oriented programming, and used C#, one of the best object-oriented programming languages, to simulate sets and their features. In addition, for each hypothesis, the author raised examples with C# codes that realize the theory in this paper, clearly showing the approach proposed in this paper and why it is both efficient and elegant.