The purpose of this Notebook is to explain the difference between convergence of an infinite sequence and convergence of an infinite series. An analogy is made with convergence of a function versus ...

We consider sequences of graphs (Gn) and define various notions of convergence related to these sequences: “left convergence” defined in terms of the densities of homomorphisms from small graphs into ...

The notion of I-Convergence is a generalization of the concept statistical convergence which was first introduced by H. Fast [1] and later on studied by J. A. Fridy [2,3] from the sequence space point ...

The purpose of this paper is to establish, paralleling a well-known result for definite integrals, the conditional convergence of a family of trigonometric sine series. The fundamental idea is to ...

Double sequence spaces extend the classical notion of sequence spaces to encompass two-indexed structures, thereby providing a robust framework for the analysis of functions and operators in ...

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches ...

Abstract: This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part ...

Abstract: Based on martingale theory in Banach space, using the limit theorem of the B-valued martingale difference sequence, a strong limit theorem for arbitrary sequence series of B-valued random ...