学术动态

#Math101^†Session 1

Time：Sep. 8, 2021, 13:30--15:30

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Mr. Shi, Mingfei (Class of 2024)

Title：Continuity and intermediate value property of functions

Abstract：There had been two myths surrounding the essence of continuous functions before the last quarter of 19th century, one being that a continuous functionmust be differentiable at a large set of points, and the other being that the intermediate value property was,in fact, equivalent to continuity. Weierstrass 1872 and Darboux 1875 proved that was not the case and constructed counter examples respectively. In this talk, we present two proofs of Darboux’s theorem, which says that any derivative has the intermediate value property, although the derivate need not be continuous.Snacks and drinks will be provided.^††

† This is a series of seminars aimed at discussing mathematical analysis and advanced algebra of undergraduate level on a weekly basis. Contact shuangshen@nwpu.edu.cn for any inquiry. For a history of this seminar, please visit https://teacher.nwpu.edu.cn/2017010194.

†† The refreshments are sponsored by a math competition mentors project, which is led by Prof. Ma, Rong. The support is gratefully acknowledged.