Universal Definitions of the Roman Factorial: Introduction to Foundational Functions and the Generalization Process

This paper introduces a new method for redefining the Roman factorial using universally applicable functions that are not expressed in closed form. We present a set of foundational functions, similar to Boolean operations, to simplify the factorial expression. Through a systematic process of generalization, termed generalization process, we aim to use these foundational functions to create recursive and non-recursive, global definitions of the Roman factorial.