Partial Komori fields and imperative Komori fields

TL;DR

This paper explores the conceptual status of 1/0 in Komori fields, contrasting mathematical conventions with computer science perspectives, and discusses implications for handling partial functions.

Contribution

It provides a comparative analysis of how 1/0 is treated in mathematics and computer science within the framework of Komori fields.

Findings

Mathematicians use a conventional approach to 1/0 in Komori fields.

A plausible logic-based account for 1/0 as undefined is challenging.

Different viewpoints influence the handling of partial functions in algebraic structures.

Abstract

This paper is concerned with the status of 1/0 and ways to deal with it. These matters are treated in the setting of Komori fields, also known as non-trivial cancellation meadows. Different viewpoints on the status of 1/0 exist in mathematics and theoretical computer science. We give a simple account of how mathematicians deal with 1/0 in which a customary convention among mathematicians plays a prominent part, and we make plausible that a convincing account, starting from the popular computer science viewpoint that 1/0 is undefined, by means of some logic of partial functions is not attainable.