What makes a theory of infinitesimals useful? A view by Klein and Fraenkel

TL;DR

This paper examines the criteria set by Klein and Fraenkel for a successful infinitesimal theory, analyzing its development over a century and the impact of Robinson's framework.

Contribution

It provides a historical analysis of the evolution of criteria for infinitesimal theories and highlights Robinson's framework role in this context.

Findings

Klein and Fraenkel's criteria focus on the Mean Value Theorem.

Robinson's framework significantly influenced the development of infinitesimal theories.

The evolution reflects changing perspectives on the feasibility of infinitesimal calculus.

Abstract

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.