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Eingegangen am lS, Juni1970Summary. Based on the structure of a finite set G of real numbers arithmetic operations on G are defined using the corresponding real operations and a subsequent mapping go with real domain and range in G. Error estimations are given related to the arithmetic on G depending on go and numerically critical situations are discussed. Especially a general floating point arithmetic is developed. A definition for simulations (on G) of real functions is given with regard for inaccuracies of arguments and results.