PERAN TEOREMA LIMIT DAN KEKONTINUAN DALAM PENGEMBANGAN ANALISIS REAL

Abstract

Real analysis is a fundamental branch of mathematics that plays a crucial role in the development of modern science and technology. Two core concepts that form the foundation of real analysis are limit theorems and continuity. These two concepts not only form the logistic framework for understanding the functions and structure of real numbers, but also serve as the basis for the development of advanced theories such as differentials, integrals, and series, including applications in science and engineering. This article aims to examine in depth the role of limit theorems and continuity in real analysis, both theoretically and practically. This research employed a literature review method, reviewing various relevant Indonesian-language textbooks and scientific articles. The results show that limit theorems and continuity play a central role in establishing the consistency of real logistic analysis, strengthening mathematical proofs, and supporting the development of advanced concepts. Therefore, a thorough understanding of limits and continuity is a crucial prerequisite for students and researchers to master real analysis comprehensively.