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Raikhola, S.S. (2025) Recent Advancements in Sequences and Series of Real Numbers: Convergence, Fractals, Chaos Theory, and Applications in Dynamical Systems. Perspectives on Higher Education, 15, 21-40.
https://doi.org/10.3126/phe.v15i02.81101

has been cited by the following article:

• TITLE: Theoretical Foundations of Sequence Convergence in Real Analysis

  AUTHORS: Cris Angelo P. Salonga, John Closter F. Olivo, Arcie Toquero De Guzman

  KEYWORDS: Real Numbers, Sequences, Convergence, Monotone Convergence Theorem, Bolzano-Weierstrass Theorem

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.6, June 29, 2026

  ABSTRACT: Convergence serves as the cornerstone of Real Analysis, providing the rigorous framework necessary for the formalization of limits, continuity, and calculus. This review paper examines the fundamental properties of real-valued sequences, with particular emphasis on the relationship between boundedness and monotonicity. Key results, including the Monotone Convergence Theorem and the Bolzano-Weierstrass Theorem, are analyzed to demonstrate how sequence behavior reflects the completeness structure of the real number system. In addition to standard definitions and proofs, the paper incorporates recursive and nontrivial examples to illustrate deeper applications of convergence. The discussion further connects classical convergence theory with modern applications in numerical analysis, dynamical systems, chaos theory, and computational mathematics. Through this synthesis, the paper highlights the continuing importance of convergence in both theoretical and applied mathematical research.