![]() ![]() From this, we can readily construct an infinite sequence of Hs and Ts which never leaves unbounded ambiguity, which is to say, there is a possible coin-flipping sequence which never produces an answer. Note that, whenever we are in a situation of unbounded ambiguity, either flipping H or flipping T must leave us in a situation of unbounded ambiguity. ![]() Let’s call this being in a situation of unbounded ambiguity. Thus, no matter what method we are using, there must exist arbitrarily long finite flip sequences which have not yet resolved into definite answers. Why is that? Because of Koenig’s lemma and the point you give, essentially, but I’ll spell it out:Ĭlearly, no fixed finite number of flips will suffice, since 3 doesn’t divide evenly into 2^n for any n. It’s interesting to note that, though the method I gave has probability 1 of eventually giving an answer, it’s impossible to design a method for doing this which is guaranteed to eventually give an answer. My method does it (with probability 1 of producing an answer), and does so more efficiently than the “Flip twice if TT, then toss out and retry” method (nothing is ever tossed out, discarding information), but can still take arbitrarily long. This establishes that you can’t do it with a fixed finite upper bound on the number of flips required. You can choose to share the URL directly or through Facebook or Twitter.If I figure correctly (which is a big “if”), no multiple of three is going to be a power of two, so I don’t see another way to work this out. If you would like to share the joy of using FS Coin with your friends and family, you could do it easily by clicking the share button (beside the logo).īe default, it will include your current coin settings, so when people click the link, they will get the same coin as yours. Or you can save it as desktop or mobile applications.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |