• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 What left to right tetration does that right to left tetration doesn't robo37 Junior Fellow Posts: 15 Threads: 6 Joined: Jun 2009 06/17/2015, 04:38 PM (This post was last modified: 06/19/2015, 10:54 AM by robo37.) Just as we can find the half-way point of a linear series of values by taking the arithmetic mean or of an exponential series by taking the geometric mean, we can use the same approach to find the between value of the set of tetrated values. Other than just putting all the hyper operations up by one the only change is that you have to put the numbers in descending order, because for example to find the middle value of 2 (2^^1) and 16 (2^^3) you take the super square root of 16^2 and not 2^16 to get to the correct answer, 4 (2^^2). What's interesting is that when using more than one value the standard right to left tetration gives us incorrect answers. For instance if we take the numbers, 2, 4 and 16 we should still expect 4 to be the half way point as there is no higher or lower numbers added to diverge the original mean. However, if put the numbers in descending order, put them into an exponent tower and take the super cube root, the function is telling us the average is just over 3, and not the correct answer of 4. If we do it the "wrong way" however and solve the exponents left to right as (16^4)^2, adjusting the super cube root function to obey the same rules, we get the correct value of 4 and as far as I can tell (please correct me if I'm wrong) it works every time, no matter the sequence. So my question is, why does left to right tetration work and right to left not, if right to left is supposed to be more mathematically sound? And is there any way you can fix it so right to left tetration averages work? Sources http://www.wolframalpha.com/input/?i=%28...5E4%29%5E2 http://www.wolframalpha.com/input/?i=x%5...284%5E2%29 EDIT: Too many typos « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post A first hires look at tetration $$\lambda = 1$$ and $$b = e$$ JmsNxn 10 278 6 hours ago Last Post: JmsNxn On the first derivative of the n-th tetration of f(x) Luknik 4 113 Yesterday, 03:35 PM Last Post: Luknik Repetition of the last digits of a tetration of generic base Luknik 10 355 10/26/2021, 10:02 PM Last Post: tommy1729 On the $$2 \pi i$$-periodic solution to tetration, base e JmsNxn 0 129 09/28/2021, 05:44 AM Last Post: JmsNxn I'm back on tetration forum sheldonison 6 537 09/25/2021, 04:13 AM Last Post: JmsNxn Using a family of asymptotic tetration functions... JmsNxn 15 3,547 08/06/2021, 01:47 AM Last Post: JmsNxn Galidakis & Extending tetration to non-integers Daniel 4 887 05/31/2021, 01:26 AM Last Post: JmsNxn Math.Stackexchange.com question on extending tetration Daniel 3 1,213 03/31/2021, 12:28 AM Last Post: JmsNxn A Holomorphic Function Asymptotic to Tetration JmsNxn 2 984 03/24/2021, 09:58 PM Last Post: JmsNxn Compartmentalizing tetration proofs Daniel 1 726 03/23/2021, 12:52 AM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)