http://ping.fm/d7SiO Meer (wiskundige) benadering (in tekst) van Graham's nummer... ---> What’s the largest number ever put to practical use in mathematics — a figure so significant that it dwarfs a centillion, a googolplex, and even the total number of atoms in the known universe?(For the record, rough calculations suggest that there are 1080 atoms in the known universe or, in the short scale notation, 100 quinvigintillion atoms. There aren’t even a googol’s worth of atoms out there.) We’re talking about Graham’s Number, G, a mathematic concept so esoteric — and so massive — that there’s no simple way to even describe the number of digits that comprise Graham’s Number, let alone the number itself. Graham’s Number is just part of the answer to the following word problem: “Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then color each of the edges of this graph using only the colors red and black. What is the smallest value of n for which every possible such coloring must necessarily contain a single-colored complete sub-graph with four vertices that lie in a plane?” Now, this Trivia Geek will be the first to admit that he has no idea what the above problem means, but it sounds impressive. As noted, Graham’s Number isn’t even the answer to this problem — which no one has yet solved. Instead, G is merely the smallest known upper bound of all the possible numbers that could answer the problem, based on existing mathematic proofs. The established lower bound is six, which is yet another example of mathematic humor. Put another way, mathematicians have proven that the answer to the above problem is a number between six and G, where G is a concept so large we can’t conventionally describe using scientific notation — not exactly narrowing it down. To write out Graham’s Number using a concise expression still requires using some rather oblique terminology, the hyper operator. In this context, G = f64(4) where f(n) = hyper(3,n + 2,3). Good luck explaining that in a bar bet, though it does explain why the Guinness Book of World Records crowned G as the Champion Largest Number. All that adds up to a serious computational conundrum — and some numerically notorious Geek Trivia. --> Geek Trivia: Double (trouble) figures | Geekend | TechRepublic.com http://ping.fm/qO1DC