A Novel Proof of the Heine-Borel Theorem

Details A Novel Proof of the Heine-Borel Theorem A Novel Proof of the Heine-Borel Theorem

2008-08-06

arxiv.org/abs/0808.0844v1

Mathematics

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Scientific paper

Every beginning real analysis student learns the classic Heine-Borel theorem, that the interval [0,1] is compact. In this article, we present a proof of this result that doesn't involve the standard techniques such as constructing a sequence and appealing to the completeness of the reals. We put a metric on the space of infinite binary sequences and prove that compactness of this space follows from a simple combinatorial lemma. The Heine-Borel theorem is an immediate corollary.

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