We show that every numerated algebra satisfying sufficiently general assumptions can be approximated by negative algebras, and we specify sufficient algebraic conditions for such approximability. Our discussion is supplemented by examples of infinite positive algebras with residually finite, positively representable enrichments. We also prove that the language of identities is not expressive enough to characterize effectively infinite abstract data types, and we show that nonconstructive algebras with recursively separable classes that are finitely defined in finitely based varieties are effectively infinite.