• Corpus ID: 16318865

A Novel Proof of the Heine-Borel Theorem

  title={A Novel Proof of the Heine-Borel Theorem},
  author={Matthew Macauley and Brian Rabern and Landon Rabern},
  journal={arXiv: History and Overview},
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. 1. The Heine… 
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