The Cantor set is a typical set in the early stage of fractal geometry.It is of great significance to trace the origin of the Cantor set for perfecting the history of fractal geometry.Under the historical background of the sprout of set theory and the strictness of real number theory,Smith constructed the original model of the Cantor set which has a positive external capacity by the motivation of dealing with the integrability of functions,the starting point is to explore the integration conditions of discontinuous functions,and the breakthrough is to find specific counter examples that do not satisfy the Riemann integral theory.On the other hand,Cantor constructed a complete but nowhere dense point set by using the representation theory of infinite series.This was due to studying the concept of derived sets as the starting point,and clarifying the density and completeness of point sets as the guidance,and exploring the specific example as the goal.Cantor's work was more in line with the trend of the mathematical development at that time than Smith's,so he won the naming right for this set.In addition,the devil's ladder,fractional dimension,Cantor dust and other fractal research objects appeared one after another under the Cantor set's influence,which lay the ideological source for the final establishment of fractal geometry.
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