Axiomatic Definition of Limit of Real-Valued Functions

TL;DR

This paper introduces an axiomatic approach to defining the limit of real-valued functions, deriving the epsilon-delta characterization from four intuitive axioms to simplify the foundational understanding of calculus.

Contribution

It presents a novel axiomatic framework that derives the epsilon-delta limit definition from four basic, intuitive statements, streamlining the foundational teaching of calculus.

Findings

Derived epsilon-delta definition from four axioms

Simplified the foundational statements of limits

Provided a new axiomatic perspective on calculus fundamentals

Abstract

We present a new way of organizing the few mathematical statements which form introduction to Calculus: the epsilon-delta characterization of the limit is now d e r i v e d from four simple, intuitive and frequently used statements, which we choose as axioms.