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 Hyperoperators [n] basics for large n dyitto Junior Fellow Posts: 13 Threads: 3 Joined: Mar 2011 03/06/2011, 03:19 PM (This post was last modified: 03/06/2011, 03:36 PM by dyitto.) (03/06/2011, 08:52 AM)bo198214 Wrote: PS: at a[n]1 = a you should add n>1Indeed, thanks for checking 1. a[2]b = a * b Proof: For b = 1: By definition a[2]1 = a = a * 1 If a[2]b = a * b for a given b, then we wish to prove that a[2](b + 1) = a * (b + 1): a[2](b + 1) = a[1](a[2]b) = a + (a[2]b) = a + (a * b) = a * (b + 1) So it is proven by induction. 2. a[3]b = a ^ b Proof: For b = 1: By definition a[3]1 = a = a ^ 1 If a[3]b = a ^ b for a given b, then we wish to prove that a[3](b + 1) = a ^ (b + 1): a[3](b + 1) = a[2](a[3]b) = a * (a[3]b) = a * (a ^ b) = a ^ (b + 1) So it is proven by induction. « 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

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