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理想元を想定した演算――数の概念（公理による演繹的数学哲学）――
https://hbg.repo.nii.ac.jp/records/2000381
https://hbg.repo.nii.ac.jp/records/200038127f920c7-0cc7-4fd3-8fc7-4377d2446660
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
58-04.pdf (983.6 KB)
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| アイテムタイプ | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
|---|---|---|---|---|---|---|---|---|
| 公開日 | 2026-03-31 | |||||||
| タイトル | ||||||||
| タイトル | 理想元を想定した演算――数の概念（公理による演繹的数学哲学）―― | |||||||
| 言語 | ja | |||||||
| タイトル | ||||||||
| タイトル | Operations Developed by the Ideal ――The Concept of Numbers （The Philosophy of Mathematics Deduced by Axioms）―― | |||||||
| 言語 | en | |||||||
| 言語 | ||||||||
| 言語 | jpn | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | 理想元 | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | ideal | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | 群の定義 | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | definition of the group | |||||||
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| 主題Scheme | Other | |||||||
| 主題 | 公理 | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | axiom | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | 分配演算 | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | distributive operation | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | 数学哲学 | |||||||
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| 主題Scheme | Other | |||||||
| 主題 | philosophy of mathematics | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | departmental bulletin paper | |||||||
| 著者 |
古川,博仁
× 古川,博仁
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| 著者（英） | ||||||||
| 姓名 | Furukawa,Hirohito | |||||||
| 言語 | en | |||||||
| 著者（英） | ||||||||
| 言語 | en | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | In this paper, I have considered operations developed by the ideal, which satisfy the axioms derived from definition of the group. I establish theorems which are logical developments resulting from operations by the ideal, for explore the philosophy of mathematics as the "foundations of mathematics." The ideal described in this paper is different from one of Takagi Sadahisa et al., and is simply the elements assumed from definition of the group. By simplifying the elements, I focused on and refined the commutative and distribution law in the concept of numbers. Regarding operations using natural numbers, I challenged myself with five examples in the final section. According to Peano's axioms, the natural numbers start with 1, then 2, 3…. Note that these are numbers generated by addition （including 0 in this paper）, but these numbers are used in multiplication too. In mathematics, there is "the axiom of the distributive" for the rings. The numbers generated by addition are naturally used for multiplication, however, in the fourth section presented on "Distributive Operation", I showed that "the simultaneous use of two operators can lead to inconsistencies." I believe that such matters are the fascinating aspect of the philosophy of mathematics when discussing the“ foundations of mathematics." | |||||||
| 言語 | en | |||||||
| 書誌情報 |
広島文化学園短期大学紀要 号 58, p. 37-50, 発行日 2025-12-25 |
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| 出版者 | ||||||||
| 出版者 | 広島文化学園短期大学 | |||||||
| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 18846769 | |||||||
| 書誌レコードID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AA12454339 | |||||||
