An intuitive proof of the Dvoretzky-Hanani theorem in R^2

Efstratios Markou

paper

An intuitive proof of the Dvoretzky-Hanani theorem in R^2

arXiv:1711.04635

Abstract

The Dvoretzky-Hanani theorem states that the general term of any perfectly divergent series in a finite dimensional space does not tend to zero. An intuitive proof is provided R2 using a construction that allows us to determine a choice of +/- such that $a_{1} + / - a_{2} + / - a_{3} + / - a_{4} ... + / - a_{n} ...$ converges to a point in the space if ||a_i|| goes to 0. Extensions to the construction are proposed for the general R^n.