Using Series to Study the Relationship between Interval Continuity and Conductance

摘要

The relation between continuity of function and conductivity is already clear in mathematical analysis. For example, if a function is continuous at some point, it may or may not be derivative at this point. However, when the function is continuous in the range, it is possible that the function cannot be induced in the interval but there is not enough counter-example or proof. Therefore, this paper takes the interval as the research object. By using the related properties of the series of Weierstrass functions, this paper gives a series of continuous but not all-pervading functions in the interval, and carries out theoretical proof, image research and analogy construction, further deepens the understanding of regional function continuity and derivability.