Introduction

The notion of infinity has captivated humanity for millennia, with its boundless nature serving as a cornerstone in mathematics and philosophy. In conventional thinking, infinity represents endlessness, a concept without limits. However, this paper proposes an alternative interpretation of infinity—one that is not limitless but bounded. Such a proposition might appear contradictory at first glance, but it stems from examining the limitations of mathematical idealization.

Mathematics, as a discipline, creates an environment of perfect abstraction. It constructs simplified, idealized models of complex realities for precise manipulation. For instance, consider the equation 1 + 1 = 2. This formulation presupposes the existence of perfectly identical entities. However, in the real world, every entity carries unique properties—no two apples are identical, no matter how similar. This discrepancy signifies a fundamental discord between mathematical abstraction and the realities of existence.

Bounded infinity

This brings us to the concept of 'bounded infinity.' While the abstract mathematical notion of infinity suggests endlessness, the manifestation of infinity in the empirical world—within the framework of existence—may be inherently bounded. This conception has several arguments based on philosophical, physical, and practical sources.

Limitations of reality

Consider the limitations of observable reality. Although mathematics allows for endless iterations and limitless numbers as a theory (in contrast to framed math), the physical universe, as we understand it, imposes certain constraints. From the speed of light (as a theory of constraint) to the total energy available in the universe, these boundaries suggest that the practical existence of infinity might be inherently limited.

Reevaluate

While the concept of 'bounded infinity' marks a significant departure from traditional interpretations, it invites us to re-evaluate the often-accepted seamless transition from mathematical abstraction to real-world application.

By recognizing the nuances and complexities inherent in our universe, we might arrive at a richer, more robust understanding of concepts like infinity—a notion that is not merely endless but also nuanced and bounded.