Aren't most proofs of the "intermediate value theorem" essentially non-constructive? http://en.wikipedia.org/wiki/Intermediate_value_theorem It's fairly easy to search for zeros of continuous functions if you have additional constraints, but for a general continuous function, you're almost forced to do an exhaustive search, which for an infinite set isn't particularly productive. At 12:04 PM 11/13/2011, Marc LeBrun wrote:
Could anyone supply me with elementary examples that illustrate the idea of a non-constructive proof, for those with a "Martin Gardner reader" level of mathematical sophistication that also has a not-too-trivial but reasonably easily-verified case? For example a non-constructive proof that some set of numbers is non-empty, along with an example of such a number that can be fairly easily checked? Thanks!