The base case is actually a special case of the induction rule, with 0 taken as a label for the "least ordinal". Since there exists no with , the expression is the empty set; the only subset of the empty set is the empty set, and therefore consists of a single surreal form lying in a single equivalence class 0.
the base case is actually a special case of the induction rule with 0 taken as a label for the "least ordinal" since there exists no with  the expression is the empty set; the only subset of the empty set is the empty set and therefore consists of a single surreal form lying in a single equivalence class 0