On Half Cauchy Sequences

TL;DR

This paper introduces half Cauchy sequences, proving their convergence is equivalent to boundedness and the half Cauchy property, and demonstrates their application with an example.

Contribution

It defines the new concept of half Cauchy sequences and establishes their convergence criteria, expanding the understanding of sequence convergence.

Findings

A sequence is convergent iff it is bounded and half Cauchy.

Provided an example demonstrating the use of half Cauchy sequences.

Abstract

In this note we introduce and define half Cauchy sequences. We prove that a sequence of real numbers is convergent if and only if it is bounded and half Cauchy. We also provide an example of how the concept may be used.