by Dan Hathaway
This article originally appeared in:
College Mathematics Journal
May, 2011
Subject classification(s):
AnalysisApplicable Course(s):
4.11 Advanced Calc I, II, & Real AnalysisHere is a technique for proving the fundamental theorems of analysis that provides a unified way to pass from local properties to global properties on the real line, just as ordinary induction passes from local implication (if true for \(k\), the theorem is true for \(k + 1\)) to a global conclusion in the natural numbers. The author demonstrates this method by proving the Intermediate Value Theorem and the Heine-Borel Theorem.
A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.
To open this file please click here.