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Denik Agustito
Universitas Sarjanawiyata Tamansiswa
Agriculture, Biological Sciences & Forestry Arts Humanities Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Economics, Econometrics & Finance Education Engineering Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Library & Information Science Materials Science & Nanotechnology Mathematics Public Health Social Sciences Other

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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers Denik Agustito; Krida Singgih Kuncoro; Istiqomah Istiqomah; Agus Hendriyanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15039

Abstract

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.
Co-Authors Agus Hendriyanto Annis Deshinta Ayuningtyas Asrika, Nila Bagas Sanyoto Betty Kusumaningrum Dafid Setiana Dafid Slamet Setiana Dafid Slamet Setiana Deri Fathurahman Arif Dewi Anggreini Dewi Anggreini Dwi Nova Lestari Ega Sri Lestari Esti Harini Esti Harini, Esti Fajar Meirani Fitria Sulistyowati Hesti Anggi Astuti Irham Taufiq Irham Taufiq, Irham istiqomah istiqomah Istiqomah Istiqomah Krida Singgih Kuncoro Krida Singgih Kuncoro Kusmanto, Benediktus Ledi, Fixaris Muhammad Irfan Muhammad Irsyad Nella Evina Marlena Puspitaningati, Ajeng Restu Hayyu Khoirunnisa Riawan Yudi Purwoko Rosafika Aziza Sri Adi Widodo Sri Adi Widodo Sukiyanto Sukiyanto Tsalitsatul Maulidah Turyanto Turyanto Yuliani, Rika