Indistinctio Per Gradus: A Metric-Free Definition of Convergence with Equivalence to Classical Convergence in Metric

This paper proposes a new definition of convergence — indistinctio per gradus(IPG) — grounded in the structure of the generalized Cantor space C. The ε-δconditions, the Cauchy completion, and the Lebesgue integral are instances ofconvergence IPG. The Dominated Convergence Theorem illustrates the simplifi-cation this brings. The equivalence theorems in Part II confirm that every metricnotion of convergence is subsumed exactly. This is a constructive and inclusivegeneralization.