Heine-Borel定理的一个新证明
A Novel Proof of the Heine-Borel Theorem
摘要：
每个开始实分析的学生都学习经典的Heine-Borel定理，即区间[0，1]是紧的。在这篇文章中，我们给出了这个结果的一个证明，它不涉及标准的技术，如构造一个序列和呼吁实数的完备性。我们把一个度量的无限二进制序列的空间，并证明了紧性，这个空间遵循一个简单的组合引理。Heine-Borel定理是一个直接推论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
