A Note on the Existence of -Supremum and -Infimum
National Academy Science Letters, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s40009-026-02401-6
- Dergi Adı: National Academy Science Letters
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Zoological Record, Natural Science Collection (ProQuest), Biological Science Database (ProQuest), Earth, Atmospheric, & Aquatic Science Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: -infimum, -supremum, Existence theorem, Hyperbolic tangent, Non-Newtonian calculus
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
This study investigates the topological order structure of the non-Newtonian real line induced by the hyperbolic tangent generator. By mapping the real line onto the bounded interval, this generator induces a specific arithmetic field, denoted as. While algebraic properties of such spaces are known, their order-theoretic foundations remain underexplored. Here, we rigorously define the -infimum and -supremum. We demonstrate that despite being represented on the bounded interval, the ordered field satisfies the Least Upper Bound property. Consequently, we characterize as a complete ordered field isomorphic to. These results provide the essential analytical basis required for constructing integration theories, such as the -Riemann integral, within this framework.