This article provides a detailed explanation of the concept of “supremum (sup)” in the context of subsets \( A\subset \mathbb{R} \) of real numbers. Specifically, it describes how the supremum is defined and its properties. By understanding the intuitive meaning, mathematical formalization, and examples, we can better grasp the significance of this important concept. What…

What is a Matrix? The term “matrix” is often used in mathematics. A matrix refers to an arrangement of numbers in a rectangular shape, enclosed by brackets. Its structure consists of “rows” and “columns.” A “row” refers to a horizontal arrangement of numbers, while a “column” refers to a vertical arrangement. The Japanese term for…

The term “函数” (hánshù in Chinese) was coined as the Chinese translation of the English word function. The character “函” was chosen because its pronunciation is phonetically similar to “function.” Combined with “数” (meaning “number”), the term “函数” was formed to represent the mathematical concept. The character “函” originally means “box” or “container,” which intriguingly…

Why Did High School Students Choose a “Complicated Method”? This fascinating example of “fixed thinking” and “solution rigidity” in mathematics education comes from a story shared by a university professor who participated in entrance exam grading. The professor was tasked with evaluating mathematics exams for humanities-track students. He was very surprised when he saw the…

The relationship between algebraic equations and the geometric shapes they define reveals a deep connection between algebra and geometry in mathematics. This article explores the zero sets of algebraic equations through concrete examples, providing a detailed explanation of the underlying mathematical structures, such as ideals and the basic concepts of algebraic geometry. A Simple Example…