A Geometric Proof to Cantor's Theorem and an Irrationality Measure for Some Cantor's Series

TL;DR

This paper presents a geometric proof of Cantor's Theorem and introduces an irrationality measure for certain Cantor series, expanding understanding of their properties through geometric methods.

Contribution

It provides a novel geometric proof of Cantor's Theorem and establishes an irrationality measure for specific Cantor series, extending previous analytical approaches.

Findings

Geometric proof of Cantor's Theorem

Irrationality measure for some Cantor series

Extension of geometric methods to number theory

Abstract

Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.