A note on exact approximations

TL;DR

This paper discusses a mathematical result related to how real numbers can be precisely approximated by rational numbers, based on Hall's theorem.

Contribution

It presents a straightforward proof concerning exact rational approximations of real numbers, expanding on Hall's theorem.

Findings

Proves a simple result about exact rational approximations

Builds on Hall's theorem to clarify approximation properties

Provides a new perspective on rational approximation of real numbers

Abstract

Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.