109 urn:lsid:arphahub.com:pub:3dc5f44e-8666-58db-bc76-a455210e8891 JUCS - Journal of Universal Computer Science jucs 0948-695X 0948-6968 Journal of Universal Computer Science 10.3897/jucs.87563 87563 Research Article Topic C - Computer Systems Organization Topic D - Software Naive Fracterm Calculus Bergstra Jan j.a.bergstra@uva.nl https://orcid.org/0000-0003-2492-506X 1 Tucker John V. https://orcid.org/0000-0003-4689-8760 2 University of Amsterdam, Amsterdam, Netherlands University of Amsterdam Amsterdam Netherlands Swansea University, Swansea, Wales Swansea University Swansea Wales

Corresponding author: Jan Bergstra (j.a.bergstra@uva.nl).

Academic editor:

2023 28 09 2023 29 9 961 987 F5A6BC1C-B0DB-5623-AE1E-F37C57E09C6D 09 06 2022 17 05 2023 Jan Bergstra, John V. Tucker This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY-ND 4.0). This license allows reusers to copy and distribute the material in any medium or format in unadapted form only, and only so long as attribution is given to the creator. The license allows for commercial use.

An outline is provided of a new perspective on elementary arithmetic, based on addition, multiplication, subtraction and division, which is informal and unique and may be considered naive when contrasted with a plurality of algebraic and logical, axiomatic formalisations of elementary arithmetic.