An investigation of kuratowski’s definition of an ordered pair

In this paper, we study the definitions of ordered pair from the point of view of Kuratowski, Wiener, Hausdorff and Morse. We first present the possible definitions of an ordered pair, and then examine the structure of the Cartesian product of sets, relations, and functions. This paper can be useful for mathematical researchers in creating new insight and better understanding of the concept of ordered pair and its related mathematical concepts, such as ordered and unordered Cartesian product, relation and function, etc.