Between addition, multiplication and beyond: hyperoperations of non-integral ranks [r-libre/4152]

Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 et Tsz Hong Ip, Tony (15 mars 2025). Between addition, multiplication and beyond: hyperoperations of non-integral ranks. Communication (sur invitation) présentée au Tomorrow's Mathematicians Today 2025, Londres.

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Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Oui
Étape de publication :	Non publié
Résumé :	Starting with the Peano axioms, we can define basic arithmetic operations via induction. For instance, multiplication (”a × b”) is the iterated application of addition (”a + b”), exponentiation (”ab”) is the iterated application of multiplication, and so on. Continuing this inductive process gives us the hyperoperation hierarchy, denoted by Hr(a, b) - the hyperoperation of rank r. For example, we say addition, multiplication and exponentiation are the hyperoperations H1,H2, and H3 respectively. Notably, hyperoperations are defined for natural numbers r, a, b. In this presentation, we will look at a possible extension of Hr(a, b) to non-integral ranks r. We will first discuss some properties of hyperoperations, which lay the ground rules to construct H3/2 - the operation between addition and multiplication. We will then extend H3/2(a, b) for non-negative real numbers a, b using various interpolation techniques, which allows us to define H5/2 as the iterated application of H3/2, and so on.
Adresse de la version officielle :	https://sites.google.com/view/ima-tmt-2025/home?au...
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	30 juin 2026 17:12
Dernière modification :	30 juin 2026 17:12

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