Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers
The purpose of this paper is to introduce the idea of how to construct transfinite numbers and study transfinite arithmetic. The research method used is a literature review, which involves collecting various sources such as scientific papers and books related to Cantorian set theory, infinity, ordin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitas Muhammadiyah Mataram
2023-07-01
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| Series: | JTAM (Jurnal Teori dan Aplikasi Matematika) |
| Subjects: | |
| Online Access: | http://journal.ummat.ac.id/index.php/jtam/article/view/15039 |
| _version_ | 1797753842020909056 |
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| author | Denik Agustito Krida Singgih Kuncoro Istiqomah Istiqomah Agus Hendriyanto |
| author_facet | Denik Agustito Krida Singgih Kuncoro Istiqomah Istiqomah Agus Hendriyanto |
| author_sort | Denik Agustito |
| collection | DOAJ |
| description | The purpose of this paper is to introduce the idea of how to construct transfinite numbers and study transfinite arithmetic. The research method used is a literature review, which involves collecting various sources such as scientific papers and books related to Cantorian set theory, infinity, ordinal or transfinite arithmetic, as well as the connection between infinity and theology. The study also involves constructing the objects of study, namely ordinal numbers such as finite ordinals and transfinite ordinals, and examining their arithmetic properties. The results of this research include the methods of constructing both finite and transfinite ordinal numbers using two generation principles. Both finite and transfinite ordinal numbers are defined as well-orderings that are also transitive sets. Arithmetic of finite ordinal numbers is well-known, but the arithmetic of transfinite ordinal numbers will be introduced in this paper, including addition, multiplication, and exponentiation. |
| first_indexed | 2024-03-12T17:23:47Z |
| format | Article |
| id | doaj.art-bf9428165c224f77bf05c381a417778f |
| institution | Directory Open Access Journal |
| issn | 2597-7512 2614-1175 |
| language | English |
| last_indexed | 2024-03-12T17:23:47Z |
| publishDate | 2023-07-01 |
| publisher | Universitas Muhammadiyah Mataram |
| record_format | Article |
| series | JTAM (Jurnal Teori dan Aplikasi Matematika) |
| spelling | doaj.art-bf9428165c224f77bf05c381a417778f2023-08-05T16:03:09ZengUniversitas Muhammadiyah MataramJTAM (Jurnal Teori dan Aplikasi Matematika)2597-75122614-11752023-07-017378179210.31764/jtam.v7i3.150397029Construction of Ordinal Numbers and Arithmetic of Ordinal NumbersDenik Agustito0Krida Singgih Kuncoro1Istiqomah Istiqomah2Agus Hendriyanto3Universitas Sarjanawiyata TamansiswaUniversitas Sarjanawiyata TamansiswaUniversitas Sarjanawiyata TamansiswaIndonesian DDR Development Center, Universitas Pendidikan IndonesiaThe purpose of this paper is to introduce the idea of how to construct transfinite numbers and study transfinite arithmetic. The research method used is a literature review, which involves collecting various sources such as scientific papers and books related to Cantorian set theory, infinity, ordinal or transfinite arithmetic, as well as the connection between infinity and theology. The study also involves constructing the objects of study, namely ordinal numbers such as finite ordinals and transfinite ordinals, and examining their arithmetic properties. The results of this research include the methods of constructing both finite and transfinite ordinal numbers using two generation principles. Both finite and transfinite ordinal numbers are defined as well-orderings that are also transitive sets. Arithmetic of finite ordinal numbers is well-known, but the arithmetic of transfinite ordinal numbers will be introduced in this paper, including addition, multiplication, and exponentiation.http://journal.ummat.ac.id/index.php/jtam/article/view/15039absolutalepharithmeticcardinalityordinaltransfinite. |
| spellingShingle | Denik Agustito Krida Singgih Kuncoro Istiqomah Istiqomah Agus Hendriyanto Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers JTAM (Jurnal Teori dan Aplikasi Matematika) absolut aleph arithmetic cardinality ordinal transfinite. |
| title | Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers |
| title_full | Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers |
| title_fullStr | Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers |
| title_full_unstemmed | Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers |
| title_short | Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers |
| title_sort | construction of ordinal numbers and arithmetic of ordinal numbers |
| topic | absolut aleph arithmetic cardinality ordinal transfinite. |
| url | http://journal.ummat.ac.id/index.php/jtam/article/view/15039 |
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