• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Tetration of 2 and Aleph_0 tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 11/13/2011, 12:09 PM (This post was last modified: 11/13/2011, 12:54 PM by tommy1729.) the large cardinals and large ordinals are very axiomatic in nature. so without proofs of bijections or the lack of bijections it is pretty hard to talk about that. ( although i do like the comments here ) in my not so humble opinion its also a matter of taste because of the above and because of the possible use of ZF©. ( which has not been proven consistant ! ) i already commented my personal large cardinal axioms ( kinda ) , but i feel it is more intresting to consider small cardinalities. to be specific : what is the cardinality of f(n) where n lies between n and 2^n ? since cardinalities are not influenced by powers card ( Q ) = card ( Q ^ finite ) we can write our question as for n <<< f(n) <<< 2^n card(f(n)) = ? the reason i dont want to get close to n or 2^n is the question : is there a cardinality between n and 2^n ? in other words : the continuum hypothesis. in stardard math and standard combinatorics , we usually do not work with functions f : n <<< f(n) <<< 2^n. but on the tetration forum they occur very often. card(floor(sexp(slog(n)+1/(24+ln(ln(n)))))) = ? card(floor(n + n^4/4! + n^9/9! + n^16/16! + ...)) = ? regards tommy1729 « 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

Users browsing this thread: 1 Guest(s)