Algorithmic Aspects

Abstract

So far, we have freely used a luxury in mathematics that is so fundamental, we often take it for granted. In any proof, if one needs to work with an object that is known or assumed to exist, one says “let x be (the object in question)” and one moves on with the proof. No work is “wasted” on thinking about how to find the object. Indeed, especially in the finite setting it is obvious that given enough patience we should be able to find the object, provided it exists. Simply try out all possibilities and one of them will work. As long as one is not interested in the object itself, this approach is very efficient, especially in ruling out blind alleys.