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This chapter introduces the concept of error function in order to quantitatively investigate errors. Error function is categorized according to the differences in the range of error values and the object of interests. Scalar and vector functions are then examined. The process of building error function is discussed based on different rules in judging errors. Last but not the least, the relationships between values of error functions under different rules of judging errors are examined. Three propositions are proposed accordingly. This chapter mainly seeks to quantify the errors in error system models, which makes it possible for the error system models to be widely applied in practice.