This paper introduces normal systems and the normal sum of general systems. A system S=(M,R) is normal if and only if any two relations in R are not contained in the same Cartesian product Mn for any ordinary number n. Normal sum is a new kind of decomposition (composition) of general systems. Given a normal system S=(M,R), and two subsets A1⊆M and A2⊆M. One of the main results is that the normal sum of the A1‐related subsystem and the A2‐related subsystem of S equals the (A1∪A2)‐related subsystem of S. This implies that every normal system is a normal sum of its subsystems which are non‐trivial and non‐discrete.
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