Embodiment of infinity in mathematics

Abstract

In this article, we discuss the embodiment of infinity as one of fundamental concepts in mathematics. In contrast to the embodiment of many other mathematical concepts, the embodiment of infinity is an endless dynamic process. In embodying +∞, an object moves rightward toward a previously-set limit and passes it. Then, a new limit is set on the right side of the moving object. The moving object continues its movement and passes it as well. The moving object can pass any limit. In other words, there is no impassable limit for it. In embodying -∞, a similar process happens but the movement is leftward. Embodiment of infinitely small quantities has a basic similarity to the embodiment of infinitely large quantities, although it is different in some respects. We call the embodiment of infinity as iterative embodiment. It is iterative because the process of setting a new limit and passing it is repeated endlessly. Finally, it is suggested that in the process of embodying infinitely large and infinitely small quantities, the visual system and the motor system play important roles, as this process involves spatial concepts and movement.