Pendekatan Epsilon-Delta terhadap Konsep dan Pembuktian Limit dalam Analisis Real
Abstract
This article aims to elaborate on function limit through the epsilon-delta approach and bridge the intuitive understanding from calculus to formal proof in real analysis. The writing of this article uses the method of literature study and conceptual analysis, by referring to standard textbooks of real analysis and relevant mathematical literature. The stages of discussion include presenting the connection between intuitive concepts and formal definitions, in-depth analysis of each component of the definition of , and concluding with a demonstration of a systematic proof framework. The article shows that the difficulties often encountered in formal proofs can be overcome through logical understanding and a two-stage process: preliminary analysis to find the right value of and formal proof for validation. The result of this discussion is a conceptual guide that confirms that mastery of the approach is a crucial competence for the successful study of advanced mathematics, particularly in real analysis.
Downloads
References
Dale Varberg. (2006). Dale Varberg, Edwin Purcell, Steve Rigdon - Calculus-Prentice Hall (2006). In Calculus (Vol. 9, pp. 1–797).
Dhombres, J. (1985). The origins of Cauchy’s rigorous calculus. In Historia Mathematica (Vol. 12, Issue 1). https://doi.org/10.1016/0315-0860(85)90078-3
Faridah, S., Umie Ruhmana Sari, S., & Malik Ibrahim Malang, M. (n.d.). Universitas Islam Negeri Maulana Malik Ibrahim Malang.
Islahul Mukmin, M., & Masamah, U. (2024). Pengembangan Bahan Ajar Digital-Interaktif Analisis Real Berbasis Moderasi Beragama untuk Mahasiswa PTKIN di Indonesia. In Academic Journal of Math (Vol. 06, Issue 01). http://journal.iaincurup.ac.id/index.php/arithmetic/index
Nicolaescu, L. I. (2019). Introduction To Real Analysis. In Introduction to Real Analysis. https://doi.org/10.1142/11553
Nirwana, N., Susanti, E., & Susanto, D. (2021). Pengaruh Penerapan Somatis, Auditori, Visual, dan Intelektual Terhadap Kemampuan Komunikasi Matematis Siswa. Ideas: Jurnal Pendidikan, Sosial, Dan Budaya, 7(4), 251. https://doi.org/10.32884/ideas.v7i4.451
Robert G. Bartle, D. R. S. (2011). Introduction to Real Analysis, Fourth Edition (Fourth). John Wiley & Sons. http://gen.lib.rus.ec/book/index.php?md5=1a7ac55b016cc56c99944370b68f1e4a
Rudin, W. (n.d.). [Walter_Rudin]_Principles_of_Mathematical_Analysis(BookFi).pdf. McGraw-Hill Science Engineering Math.
Copyright (c) 2025 Ahmad Maulana Firmansyah
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
