#Math101 Session 36

Time：Mar. 26, 2026, 14:00-16:00

Location：D212 Hai Tian Building, Chang'an Campus

Speaker：Mr. Sun, Wenhao (Class of 2024)

Title：Completeness and convergence on the real line

Abstract：In this talk, we first present several classical formulations equivalent to the completeness axiom of the real numbers, including theorems of Cauchy-Cantor, Borel-Lebesgue, and existence of suprema/infima. We then introduce the Dedekind cuts as a rigorous method for constructing the real number system from the rational numbers, thereby formalizing the intuitive notion of “filling the gaps”. Finally, we will discuss the notions as well as basic properties of limit, series, and Cauchy sequences, both on the real line and in the broader setting of metric spaces.

（文：申爽/审核：郭千桥）