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 Tetration and higher-order operations on transfinite ordinals quickfur Junior Fellow Posts: 22 Threads: 1 Joined: Feb 2008 03/29/2008, 04:01 PM bo198214 Wrote:[...] Just skimmed through your article and asking myself how this function can be expressed with a recursive definition ...I've not thought about that... but I assume it must be possible since the algorithm obviously can be expressed as a Turing machine, so it must be recursive. I'm not sure how exactly to go about deriving a recursive definition for it, though. Maybe one way is to perform a depth-first traversal on the tree, left child first, and recursively linearize the left-most children. So, in computer pseudocode, it could be something like this: Code:```linearize(T,m) {     if (is_rightbranching_chain(T.left_subtree) and         is_rightbranching_chain(T.right_subtree))     {         ... (perform the transformation... not sure how to express this recursively yet)     } else {         T.left_subtree = linearize(T.left_subtree, m);         T.right_subtree = linearize(T.right_subtree, m);         return T;     } }``` Once we work out the pseudocode, maybe there's a way to factor it into a recursive function...? « Next Oldest | Next Newest »

 Messages In This Thread Tetration and higher-order operations on transfinite ordinals - by quickfur - 02/21/2008, 08:16 PM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 02/23/2008, 03:33 AM RE: Tetration and higher-order operations on transfinite ordinals - by GFR - 02/23/2008, 09:47 AM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 02/23/2008, 05:46 PM RE: Tetration and higher-order operations on transfinite ordinals - by GFR - 02/26/2008, 09:33 AM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 03/28/2008, 10:55 PM RE: Tetration and higher-order operations on transfinite ordinals - by bo198214 - 03/29/2008, 09:58 AM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 03/29/2008, 04:01 PM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 08/16/2008, 01:58 AM

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