• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 the inverse ackerman functions JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 04/14/2011, 08:48 PM (This post was last modified: 04/14/2011, 08:54 PM by JmsNxn.) Every one here has heard of the ackermann function; we'll define it as: $\{x,\, y,\, u\, \epsilon\, R^{+}\}$ $A(x,\, y,\, u)\, =\, x\, \{u\}\, y$ I'm interested in itss inverses though. There would be three inverses therefore, the first one with relation to x: $R(x,\, y,\, u)\, =\, x\, \}u\{\, y$ which means R for roots, and }u{ is taken to mean: }0{ is subtraction, }1{ division, }2{ roots, }3{ super roots, etc etc and then are next inverse is taken with relation to y $L(x,\, y,\, u)\, =\, u;\log_x(y)$ where 0;log_x(y) = y-x, 1;log_x(y) = y/x, and 2;log_x(y) = $\log_x(y)$ and now, the final inverse, and definitely the most interesting inverse is the inverse taken with relation to u $I(x, y, u) = ?$ if $A(x, y, I(x, y, u)) = u)$ this question is the equivalent of asking $3\,\{u\}\, 4\, =\, 9$ what is u? it's the act of rearranging an equation to solve for u. It might even seem intuitively impossible. I've only found one solution to this problem... and that's by using logarithmic semi operators, though I is only defined over domain [0, 2] Does anyone know if anybody else has ever looked into this inverse function? « Next Oldest | Next Newest »

 Messages In This Thread the inverse ackerman functions - by JmsNxn - 04/14/2011, 08:48 PM RE: the inverse ackerman functions - by tommy1729 - 04/14/2011, 10:57 PM RE: the inverse ackerman functions - by JmsNxn - 04/14/2011, 11:04 PM RE: the inverse ackerman functions - by Xorter - 09/18/2016, 11:02 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Inverse Iteration Xorter 3 3,312 02/05/2019, 09:58 AM Last Post: MrFrety Inverse super-composition Xorter 11 15,260 05/26/2018, 12:00 AM Last Post: Xorter The AB functions ! tommy1729 0 1,848 04/04/2017, 11:00 PM Last Post: tommy1729 Look-alike functions. tommy1729 1 2,360 03/08/2016, 07:10 PM Last Post: hixidom Inverse power tower functions tommy1729 0 2,135 01/04/2016, 12:03 PM Last Post: tommy1729 [2014] composition of 3 functions. tommy1729 0 2,014 08/25/2014, 12:08 AM Last Post: tommy1729 The inverse gamma function. tommy1729 3 8,515 05/13/2014, 02:18 PM Last Post: JmsNxn Intresting functions not ? tommy1729 4 5,788 03/05/2014, 06:49 PM Last Post: razrushil generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 24,814 11/24/2011, 01:18 AM Last Post: JmsNxn Discrete-analytic functions Ansus 4 6,262 07/30/2011, 04:46 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)