Mathematical induction, transfinite induction, and induction over the continuum
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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.
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Agustito, D., Sukiyanto, S., & Kuncoro, K. S. (2023). Mathematical induction, transfinite induction, and induction over the continuum. International Journal of Mathematics and Mathematics Education, 1(2), 180–191. https://doi.org/10.56855/ijmme.v1i02.385
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