The paper addresses Leon Henkin's proposition as a "lighthouse", <br>which can elucidate a vast territory of knowledge uniformly: logic, set theory, <br>information theory, and quantum mechanics: Two strategies to infinity are <br>equally relevant for it is as universal and thus complete as open and thus incomplete. <br>Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' <br>proposition are reformulated so that both completeness and incompleteness to <br>be unified and thus reduced as a joint property of infinity and of all infinite sets. <br>However, only Henkin's proposition equivalent to an internal position to <br>infinity is consistent . This can be retraced back to set theory and its axioms, <br>where tha t of choice is a key. Q...