Exiron number

Exiron numbers are a proposed extension of the number system designed to formally represent division by zero as a distinct mathematical object rather than an error. In this framework, expressions involving division by zero are treated as meaningful entities that carry information about the undefined component instead of collapsing the entire expression.The key idea is to separate the ordinary, finite part of a number from its division-by-zero contribution and allow consistent algebraic operations on such objects. Addition, subtraction, and multiplication are defined so that the division-by-zero component is preserved and transformed in a predictable way, making calculations stable rather than contradictory.Exiron numbers do not claim that division by zero becomes finite or conventional. Instead, they offer a structured way to track and manipulate undefined behavior. The system is exploratory and incomplete, but it aims to provide a new language for studying singularities, limits, and mathematical structures where division by zero naturally appears.