# From Pythagoreans and Weierstrassians to true infinitesimal calculus

## TL;DR

This paper discusses a teaching approach for infinitesimal calculus that emphasizes comparing different definitions of concepts like continuity and convergence, which students find more appealing than traditional epsilon-delta definitions.

## Contribution

It introduces a comparative teaching method for infinitesimal calculus that highlights multiple definitions to enhance student understanding and engagement.

## Key findings

- Students prefer infinitesimal definitions over epsilon-delta ones.
- The teaching method improves conceptual understanding of calculus.
- Poll results favor the infinitesimal approach.

## Abstract

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting "the definition" to the students as a monolithic absolute. We hope that this could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon, delta ones.