Transfinite induction can be classified as either a theorem or an axiom, depending on the logical system in use. In any system, a statement can be treated as an axiom, though this may require dropping another axiom to maintain minimality. Conversely, it can also be considered a theorem, which might necessitate the addition of another axiom for proof. The classification ultimately hinges on the foundational framework being applied. Thus, the status of transfinite induction is context-dependent.