The IEEE 754 floating-point standard, foundational to modern computing since 1985, treats division by zero as an undefined operation, returning error states or special infinity values. This convention, while practically expedient, creates mathematical discontinuities and computational barriers across multiple domains. We propose IEEE DZ20i, a continuous extension of IEEE 754 based on the axiom a/0 = a, which maintains computational continuity through zero-valued divisors.This paper presents the mathematical foundation of the DZ20 axiom, demonstrates its consistency within a Meta-Framework for Adapted Mathematics (MCMA), specifies the IEEE DZ20i standard including symmetric human-AI co-validation mechanisms, and explores applications across algorithmic computing, energy systems, hardware design, robotics, and space exploration.Implementation results show that IEEE DZ20i eliminates a broad class of runtime exceptions while preserving backward compatibility with IEEE 754 operations outside the zero-divisordomain.