Bijectivism — Making Every Function Reversible

Abstract:

We propose Bijectivism, a framework in which every mathematical function has a well‑defined inverse when that inverse is allowed to be set‑valued. Traditionally, a function is called “invertible” only if it is bijective—that is, only if its inverse is single‑valued. This convention unnecessarily restricts our conceptual toolkit and forces piecewise patches (domain restrictions, branch cuts) where a more natural, uniform treatment is possible.