Archive for August 16th, 2008

Just-do-it proofs

August 16, 2008

This post is another sample Tricks Wiki article, which revisits a theme that I treated on my web page. Imre Leader pointed out to me that I hadn’t completely done justice to the idea, and that the notion of a “just-do-it proof” had some more specific features that I had not sufficiently emphasized. His opinion matters to me since he was the one who told me about the concept. He himself got it from Béla Bollobás: I don’t know whether it goes further back than that. This is a second attempt at explaining it. Imre, if there’s anything you don’t like about this one, then please edit it when it appears on the Tricks Wiki.

Title: Just-do-it proofs.

Quick description: If you are asked to prove that a sequence or a set exists with certain properties, then the best way of doing so may well be not to use any tricks but just to go ahead and do it: that is, you build the set/sequence up one element at a time, and however you do so you find that it is never difficult to continue building. (more…)