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 Tetration and higher-order operations on transfinite ordinals quickfur Junior Fellow Posts: 22 Threads: 1 Joined: Feb 2008 03/28/2008, 10:55 PM (This post was last modified: 03/28/2008, 10:57 PM by quickfur.) Dear All, After further research into the correspondence between (countable) ordinals and functions, I believe I have discovered the function that represents a growth rate corresponding to the Feferman-Schütte ordinal $\Gamma_0$. The details are here: http://eusebeia.dyndns.org/veblen/etf.html Interestingly enough, the function turns out to be related to transforming binary trees. In particular, the diagonalized function E(n) involves transforming a left-branching linear chain to a right-branching linear chain, and in the process adding many nodes... MANY nodes (so many that I suspect it's not possible to describe using any other known notation for large numbers). All this is done by a very simple-looking two-step transform, applied repeatedly until the tree becomes a right-branching chain. Anyway, let me know what y'all think. P.S. Oh, and I should add that even though I derived the function based on the structure of transfinite ordinals, the function itself has no direct connection with ordinals. It's really just a binary tree transforming function. (Just so the anti-Cantorians here don't write it off as uninteresting. ) « 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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