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IV Inconsistency of the empty and the transfinite Set

April 2022. The empirical proof is provided that the axiom that requires the empty set contradicts reality. The contradiction with nature also applies to Cantor's idea of the transfinite, as Hilbert has acknowledged. Accordingly, empty and transfinite sets are based on rationalistic theories that contradict empiricism and are therefore necessarily wrong. However, Hilbert did not draw this conclusion but demanded the mathematical consistency of the transfinite. The formal proof that the transfinite set does not exist requires the refutation of the ZFC-axiom of infinity. This axiom presupposes the empty set, that according to empirical evidence does not exist. The axiom of infinity is therefore contradictory. The empty set does not appear in Cantor's doctrine, ZFC contradicts Cantor.