Not sure if this is exactly on point, but: It's an easy theorem in topology that any continuous function f: [0,1] -> [0,1] has a fixed point. But this says nothing about how to find it. If, however, it's known that there is a number c with 0 < c < 1 such that for all x,y in [0,1] we have |f(x) - f(y)| <= c |x - y|, then it's easy to show that for any x in [0,1] the sequence x, f(x), f(f(x)), . . . must converge to a fixed point. --Dan Marc 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?
Even though kleptomaniacs can't help themselves, they do.