How the continuum hypothesis could have been a fundamental axiom

TL;DR

The paper presents a thought experiment illustrating how the continuum hypothesis could have been adopted as a fundamental axiom, emphasizing its potential necessity for mathematics and calculus development.

Contribution

It offers a novel perspective on the historical and conceptual origins of considering the continuum hypothesis as a core mathematical axiom.

Findings

Highlights the importance of the continuum hypothesis in mathematical foundations

Suggests a hypothetical historical pathway for its acceptance as an axiom

Provides insights into the role of axioms in mathematical development

Abstract

I describe a simple historical thought experiment showing how we might have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensable even for calculus.