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Date
2023-12Type
- Journal Article
ETH Bibliography
yes
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Abstract
In this paper three main results are presented: a bijection between natural sums and natural products, the completion of the axioms of Carruth for natural sums, and a new characterization of the natural sums in terms of Klaua’s integral ordinals. After introducing some preliminary results, we present two lemmas and a proposition for the proof of the existence of a bijection between natural products and natural sums. Then we prove the incompleteness of Carruth’s axioms by providing two counterexamples, and complete Carruth’s axioms by adding a fifth axiom. Finally, we introduce a characterization of natural sums in terms of Klaua’s integral ordinals and present two families of natural sums, which differ from Hessenberg’s sum. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000637410Publication status
publishedExternal links
Journal / series
European Journal of MathematicsVolume
Pages / Article No.
Publisher
SpringerSubject
Ordinal numbers; Arithmetic; Hessenberg sum; Carruth axiomsOrganisational unit
08848 - Halbeisen, Lorenz (Tit.-Prof.) / Halbeisen, Lorenz (Tit.-Prof.)
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ETH Bibliography
yes
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