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

Efstratios Markou

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arXiv · 1711.04635

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

Efstratios Markou

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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.

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Efstratios Markou. 2017-11-07. An intuitive proof of the Dvoretzky-Hanani theorem in R^2. https://arxiv.org/abs/1711.04635

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