Properties of The Algebraic Structure of Real Number Sequences Bagus Aqil Saputra (a*), Ikrar Pramudya (a), Mardiyana(a), Ponco Sujatmiko (a), Dyah Ratri Aryuana (a)
a) Department of Mathematics Education, Universitas Sebelas Maret, Jl. Ir. Sutami No.36, Kentingan, Jebres, Surakarta, Jawa Tengah 57126, Indonesia, Telp/Fax: 0271-648939
*bagusaqilsaputra[at]student.uns.ac.id
Abstract
The real number sequence has practical value for studying various topics in real analysis. This study aimed to characterize the algebraic structure of the set of real number sequences with addition and function multiplication as its binary operation. Therefore, the discussion of problems in this study utilized properties from group theory and real analysis to derive properties of the elements and subsets. The investigated problems included the properties of the set of real number sequences based on convergence, the existence of subgroups, normal subgroups, and group homomorphisms. The methods utilized in this research involved literature review and deductive mathematical proofs to obtain relevant theorems. Based on the problem, the concepts and theories used for analysis were those related to group theory and properties of real number sequences in real analysis. Therefore, the concepts and theories relevant to the topic needed to be reconsidered in order to obtain relevant concepts and theories to solve the research problem.
Keywords: sequence- convergence- normal subgroup- homomorphism
