Abstract: In this paper we proposed the concepts of the number set with all partial sums unequal and the number set with a part of partial sums unequal. The constructive theorems and properties of such number sets are given and related calculation formulas have been worked out. It has been proved that under special conditions geometrical sequence is a number set with all partial sums unequal. At last, some application, examples of such number sets in developing electronic brain for traditional Chinese medicine, computer information processing of Chinese characters and industrial quality check are given.