Functional analysisFunctional analysis is fundamental to systems engineeringSystems engineering, where complex systemsComplex systems are decomposed into functions that describe transformations from inputs to outputs. These functions are fundamental to system realization—they guide architectural decisions, enable requirements allocation, shape physical implementation, and determine system capabilities. In systems engineeringSystems engineering, determining whether two functions are truly equivalent remains a significant challenge. While functional equivalenceFunctional equivalence might seem straightforward, its implications run deeper than simple input–output comparisons. This paper establishes the foundation for understanding the nature of functional equivalenceFunctional equivalence by exploring real-world examples that demonstrate why a formal theory is needed. We examine common misconceptions, challenges, and consequences of inadequate equivalence understanding. Through carefully chosen examples, we demonstrate key conditions that influence functional equivalenceFunctional equivalence and justify the need for a formal theoretical framework based on systems theorySystems theory, set theorySet theory, and propositional logicPropositional logic. The paper concludes by presenting preliminary theorems, setting the stage for a comprehensive theory of functional equivalenceFunctional equivalence.