• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Hyperoperators [n] basics for large n dyitto Junior Fellow Posts: 13 Threads: 3 Joined: Mar 2011 03/06/2011, 08:56 PM 5a. a > 1 -> a[n]b > b 5b. a > 1 -> a[n](b + 1) > a[n]b Proof: For n = 1 & 2 5a and 5b are evident. Let's assume 5a and 5b to be true for a given n > 1 ==> (i). Proof of 5a for n + 1: a [n+1] 1 = a and so a [n+1] 1 > 1 Now assume a [n+1] b > b for some b a [n+1] (b + 1) = a [n] (a [n+1] b) > a [n] b (Since (i) says: x > y -> a [n] x > a [n] y) Furthermore a [n] b >= b + 1, so: a [n+1] (b + 1) > b + 1 So 5a has been proven for n + 1 by induction applied to b Proof of 5b for n + 1: a [n+1] (b + 1) = a [n] (a [n+1] b) > a [n+1] b (Since (i) says: a [n] x > x) So 5a and 5b have been proven for any n by induction applied to n. « Next Oldest | Next Newest »

 Messages In This Thread Hyperoperators [n] basics for large n - by dyitto - 03/06/2011, 01:20 AM RE: Hyperoperators [n] basics for large n - by bo198214 - 03/06/2011, 08:52 AM RE: Hyperoperators [n] basics for large n - by dyitto - 03/06/2011, 03:19 PM RE: Hyperoperators [n] basics for large n - by dyitto - 03/06/2011, 03:24 PM RE: Hyperoperators [n] basics for large n - by dyitto - 03/06/2011, 03:32 PM RE: Hyperoperators [n] basics for large n - by dyitto - 03/06/2011, 08:56 PM RE: Hyperoperators [n] basics for large n - by dyitto - 03/06/2011, 09:41 PM RE: Hyperoperators [n] basics for large n - by dyitto - 03/07/2011, 11:26 AM RE: Hyperoperators [n] basics for large n - by bo198214 - 03/07/2011, 01:35 PM RE: Hyperoperators [n] basics for large n - by dyitto - 03/12/2011, 10:19 PM

 Possibly Related Threads... Thread Author Replies Views Last Post All Maps Have Flows & All Hyperoperators Operate on Matrices Daniel 0 300 03/14/2020, 06:22 AM Last Post: Daniel Interesting commutative hyperoperators ? tommy1729 0 352 02/17/2020, 11:07 PM Last Post: tommy1729 Iteration basics Ivars 27 29,352 01/02/2017, 05:21 PM Last Post: Xorter Logic hyperoperators hixidom 0 1,702 10/14/2015, 08:26 PM Last Post: hixidom Theorem in fractional calculus needed for hyperoperators JmsNxn 5 7,526 07/07/2014, 06:47 PM Last Post: MphLee 2 [n] b and 3 [n] b for (large) integer n, b dyitto 2 4,254 03/12/2011, 10:52 PM Last Post: dyitto Hyperoperators Mr. Pig 4 6,099 06/20/2010, 12:26 PM Last Post: bo198214

Users browsing this thread: 1 Guest(s)