Hyperreal Numbers for Infinite Divergent Series

TL;DR

This paper explores how hyperreal numbers can be used to rigorously handle divergent series, addressing longstanding issues in mathematics related to infinities and contradictions within the real number system.

Contribution

It introduces the application of hyperreal numbers as a new framework for managing divergent series, offering a more consistent mathematical approach.

Findings

Hyperreal numbers alleviate contradictions in divergent series.

A new framework for handling infinities in mathematics.

Enhanced understanding of divergent series through hyperreals.

Abstract

Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent series in a more comprehensive and tractable way.