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 Tetration of 2 and Aleph_0 jht9663 Junior Fellow Posts: 3 Threads: 1 Joined: Aug 2011 09/07/2011, 03:33 PM So essentially [\$\aleph_{\aleph_{0}}+1=\aleph_{\aleph_{0}}\$], [\$2*\aleph_{\aleph_{0}}=\aleph_{\aleph_{0}}\$], [\$2^\aleph_{\aleph_{0}}=\aleph_{\aleph_{0}}\$], and 2^^[\$\aleph_{\aleph_{0}}=\aleph_{\aleph_{0}}\$]. However I do not agree that [\$\aleph_{\aleph_{1}}] does not exist. My heuristic reasoning is: 1 (the first integer past the addition identity) + 0 = 1 (the first integer past 0) (assuming the Continuum Hypothesis) 2 (the first integer past the exponentiation identity) ^ [\$\aleph_{0}\$] = [\$\aleph_{1}\$] (1 being the first integer past 0) if these are true then 2 (the first integer past the pentation identity) ^^^ [\$\aleph_{\aleph_{0}}\$] = [\$\aleph_{\aleph_{1}}\$] (1 being the first integer past 0) and you could extend the pattern. Of course I have no other reasons to believe that the third statement is true, as one would have to prove that there does not exist a bijection from [\$\aleph_{\aleph_{0}}\$] to 2^^^[\$\aleph_{aleph_{0}}\$]. Also, where would be a place I could go to on the internet to find more discussion on this topic? Thanks, Hassler Thurston « Next Oldest | Next Newest »

 Messages In This Thread Tetration of 2 and Aleph_0 - by jht9663 - 09/06/2011, 03:47 PM RE: Tetration of 2 and Aleph_0 - by JmsNxn - 09/06/2011, 09:28 PM RE: Tetration of 2 and Aleph_0 - by tommy1729 - 09/07/2011, 03:37 AM RE: Tetration of 2 and Aleph_0 - by jht9663 - 09/07/2011, 03:33 PM RE: Tetration of 2 and Aleph_0 - by sheldonison - 09/07/2011, 08:47 PM RE: Tetration of 2 and Aleph_0 - by sheldonison - 09/09/2011, 05:54 PM RE: Tetration of 2 and Aleph_0 - by jht9663 - 09/07/2011, 03:34 PM RE: Tetration of 2 and Aleph_0 - by tommy1729 - 09/10/2011, 12:22 PM RE: Tetration of 2 and Aleph_0 - by tommy1729 - 11/13/2011, 12:09 PM

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