The authors investigate carefully whether or not two classes of inference algorithms, which are Compositional Rule of Inference (CRI) proposed by L.A.Zadeh and Triple-Implication algorithm (Triple-I) proposed lately, hold the continuity and approximation properties, and moreover, also how the approximation errors are propagated by them. Therefore, a fuzzy inference algorithm is viewed as a mapping from one fuzzy set to another, Hamming distance formula is used as the computing distance between the two fuzzy sets. The authors prove that the two classes of algorithms hold the continuity properties in the cases of fuzzy modus ponens and fuzzy modus tollens. The authors also point out that Triple-I algorithm always holds the approximation property if antecedent and consequence of the known rule are normal fuzzy sets. However CRI algorithm holds approximation property only if CRI holds consistency property. Two classes of algorithms do not make approximation errors magnified when they hold approximation property. The results of the paper are useful for the selection and analysis of algorithms for fuzzy inference when practical fuzzy control and expert systems are designed.