{
  "abstract": "‎The sequence space of all real-valued sequences‎, ‎denoted $Seq(\\mathbb{R})$‎, ‎is typically investigated through the lens of infinite-dimensional vector spaces‎, ‎utilizing Banach space norms or Schauder bases‎. ‎This work proposes a complementary‎, ‎constructive classification based instead on the asymptotic limit profile encoded by the pair $(\\liminf a_n‎, ‎\\limsup a_n)$‎. ‎We demonstrate that this perspective naturally partitions $Seq(\\mathbb{R})$ into seven mutually disjoint macroscale blocks‎, ‎covering behaviors from finite convergence to bounded and unbounded oscillation‎. ‎For each block‎, ‎we provide explicit closed-form representative sequences and establish that every constituent class possesses the cardinality of the continuum‎. ‎Furthermore‎, ‎we investigate the structural relationships between these blocks at two distinct levels of granularity‎. ‎At the macroscale‎, ‎we employ injective mappings to define an idealized connectivity graph‎, ‎while at the microscale‎, ‎we introduce a connection relation governed by the Hadamard (pointwise) product‎. ‎This dual analysis reveals a rich directed graph structure where the block of finite convergent sequences functions as both the only subspace and as a global attractor with no outgoing connections‎. ‎Statistical comparisons between the idealized and realized adjacency matrices indicate that the pointwise product structure realizes approximately two-thirds of the theoretically possible macroscale relations‎. ‎Ultimately‎, ‎this partition-based framework endows the seemingly chaotic space $Seq(\\mathbb{R})$ with a transparent‎, ‎geometrically interpretable internal structure‎.",
  "abstract_shown": true,
  "affiliations": [
    "‎PhD‎, ‎PStat,‎ Biostatistics Division,‎ Dalla Lana School of Public Health, University of Toronto,Toronto‎, ‎ON‎, ‎Canada"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mohsen Soltanifar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1h8qp2a5a2g98.bib",
  "cited_by": 0,
  "doi": "10.22052/mir.2026.259151.1595",
  "fulltext_url": null,
  "id": "1h8qp2a5a2g98",
  "issns": [
    "2476-4965"
  ],
  "landing_url": "https://doi.org/10.22052/mir.2026.259151.1595",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://mir.kashanu.ac.ir/article_115878_149c789ee5871a0fd005d32fd59f7bbf.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "University of Kashan",
  "ris": "https://research.draconitic.com/paper/1h8qp2a5a2g98.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:41Z",
      "native_id": "6fb0d38efd1048779c1b8964e3905759",
      "source": "doaj",
      "url": "https://doi.org/10.22052/mir.2026.259151.1595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "A Classification of Elements of Sequence Space $Seq(\\mathbb{R})$",
  "title_text": "A Classification of Elements of Sequence Space Seq(ℝ)",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:41Z",
  "url": "https://research.draconitic.com/paper/1h8qp2a5a2g98",
  "venue": "Mathematics Interdisciplinary Research",
  "versions": []
}