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All Journal International Journal of Mathematics and Mathematics Education (IJMME)
Denik Agustito
University of Sarjanawiyata Tamansiswa
Mathematics

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Mathematical induction, transfinite induction, and induction over the continuum Denik Agustito; Sukiyanto Sukiyanto; Krida Singgih Kuncoro
International Journal of Mathematics and Mathematics Education Vol. 1 No. 2 (2023)
Publisher : EDUPEDIA Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (369.617 KB) | DOI: 10.56855/ijmme.v1i02.385

Abstract

This article examines three types of induction methods in mathematics: mathematical induction, transfinite induction, and induction over the continuum. If a statement holds true for all natural numbers, it is proven using mathematical induction. If a statement holds true for all ordinal numbers, it is proven using transfinite induction. Since induction over the continuum cannot be applied to a statement, when something is said to be proven true for every point in [a, b), the proof is done using induction over the continuum.
Co-Authors Krida Singgih Kuncoro Sukiyanto Sukiyanto