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 the logical hierarchy tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 02/08/2009, 04:16 PM here i present what is according to me the " logical hierarchy " i found it important to say , because it appears often on math forums and is usually stated or ordered in a way i disagree with. no tetration or non-commutativity. no ' popularized ' ackermann or buck. but plain good old logic in my humble opinion. most imporant is the existance of a single neutral element f_n ( a , neutral ) = f_n ( neutral , a ) = a for all a ! 1) a + b 2) a * b 3) a ^ log(b) to see how i arrived at 3 : a ^ log(b) = b ^ log(a) = exp( log(a) * log(b) ) 4) exp ( log(a) ^ log(log(b)) ) to see how i arrived at 4 : note that 3) is used upon log(a) and log(b). etc etc note that the neutral elements are 1) addition -> 0 2) multiplication -> 1 3) a ^ log(b) -> e 4) -> e^e 5) -> e^e^e 6) -> e^e^e^e etc « Next Oldest | Next Newest »

 Messages In This Thread the logical hierarchy - by tommy1729 - 02/08/2009, 04:16 PM RE: the logical hierarchy - by bo198214 - 02/08/2009, 10:25 PM RE: the logical hierarchy - by tommy1729 - 02/08/2009, 10:45 PM RE: the logical hierarchy - by bo198214 - 02/08/2009, 10:53 PM

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