A concrete description of terminal coalgebras, T , of all finitary endofunctors of Set is presented: each such a functor is a quotient of the polynomial endofunctor of some finitary signature Σ modulo some "basic" equations. Then T can be described as the algebra of all infinite Σ-labeled trees modulo the congruence obtained by applying the basic equations finitely or infinitely many times (a concept defined below). As a consequence, free iterative theories in the sense of Calvin Elgot are

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... ibed over all finitary endofunctors of Set: they are the theories of all rational Σ-labeled trees (i.e., trees having only finitely many subtrees) modulo the above congruence.