The challenge of transfinite compassion lies in the mathematical incompatibility of three intuitive desiderata: efficiency (Strong Pareto), equity (Anonymity), and consistency (Transitivity or Continuity). When agent sets are infinite, these principles collide, leading to a landscape defined by no-go theorems. Foundational results like Diamond’s trilemma and the Basu-Mitra impossibility theorem demonstrate that no real-valued social welfare function can treat infinite generations both fairly and efficiently without sacrificing topological regularity or representability.