Nobody needs equations

TL;DR

This paper demonstrates how standard mathematics can be performed without equations and introduces a foundational framework where equations are not even formulatable, with implications for quantum mechanics and indiscernibility.

Contribution

It introduces a simple foundational framework that excludes equations from standard mathematics and applies it to quantum mechanics and indiscernibility issues.

Findings

Mathematics can be developed without equations.

A foundational framework without equations is possible.

Application to quantum mechanics and indiscernibility issues.

Abstract

Equations are ubiquitous in most mathematical activities. Nevertheless, in this paper it is shown how to do standard mathematics without any equation at all. More than that, it is proven there is a foundational framework for standard mathematics where equations cannot be even written, in the sense they are not formulas. The proof of those claims is very simple, almost obvious. I use this framework to suggest a way to deal with certain notions of indiscernibility between `objects', with special emphasis on some aspects of quantum mechanics. Finally I compare this approach to quasi-set theory, an unnecessarily complicated formal work designed to deal with violation of Leibniz Principle of the Identity of Indiscernibles.