Comments on: CH. Rayo’s Number! http://mathfactor.uark.edu/2007/04/ch-rayos-number/ The Math Factor Podcast Site Fri, 08 Aug 2014 12:52:06 +0000 hourly 1 https://wordpress.org/?v=4.9.25 By: Al Downing http://mathfactor.uark.edu/2007/04/ch-rayos-number/comment-page-1/#comment-848 Wed, 16 Feb 2011 16:21:21 +0000 http://mathfactor.uark.edu/2007/04/15/ch-rayos-number/#comment-848 First, how far does Rayos number surpass a meameamealokkapoowa oompa?. Second, the fact the Rayos number is in the Busy Beaver Function, are there ANY other computable functions which are beyond the Busy Beaver Function?.

]]> By: strauss http://mathfactor.uark.edu/2007/04/ch-rayos-number/comment-page-1/#comment-56 Sun, 15 Apr 2007 18:02:07 +0000 http://mathfactor.uark.edu/2007/04/15/ch-rayos-number/#comment-56 The Busy Beaver Function, mentioned in this segment, is really quite amazing; one particularly mind-blowing property is that it grows faster than any computable function!!!

(More correctly, no computable function bounds the busy beaver function; i.e. anything you can actually compute, in any way whatsover, will sooner or later be topped by the Busy Beaver!!) We’re planning to come back to this paradoxical sounding statement in a later segment…

But that was just a way-station on the way to Rayo’s number, which is vastly larger than anything you can easily name: essentially, he calls for the biggest number that takes a googol’s worth of symbols to notate, in any well-defined way, and then tops that!

As we saw last week, Graham’s number only takes, maybe, a hundred symbols to write out, so it is hard to get a handle on what Rayo’s number might be!

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