The Theory of Integral and Differential Infinity. 1. Conceptualization

The theory of integral and differential infinity (TIDI) is introduced. The principle of integral infinity refers to the accumulation of value (numbers, mass, attractive forces, etc.), while the principle of differential infinity involves the division of value (numbers, mass, repulsive forces, etc.). Historical conceptualizations of infinity are shown to conform to the principles of integral and differential infinity although in many instances they conflate the two types of infinity and in others lead to erroneous conclusions. The principles of integral and differential infinity can be combined as linear combinations of simple expressions, forces, and special functions to formulate TIDI. TIDI provides a basis for explaining physical phenomena that are well known or currently inexplicable.