Tetration Forum › Tetration and Related Topics › Hyperoperations and Related Studies v
Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp

Threaded Mode
Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp
JmsNxn Offline
Ultimate Fellow
*****
Posts: 1,214
Threads: 126
Joined: Dec 2010
#21
04/14/2011, 11:16 PM (This post was last modified: 04/14/2011, 11:16 PM by JmsNxn.)
I think the easiest proof is

\( f(x^y) = f(x)f(y) = f(y^x) \)

which can only be true for a constant function.
Find
Reply
bo198214 Offline
Administrator
Posts: 1,631
Threads: 107
Joined: Aug 2007
#22
04/15/2011, 07:29 AM
(04/14/2011, 11:16 PM)JmsNxn Wrote: I think the easiest proof is

\( f(x^y) = f(x)f(y) = f(y^x) \)

which can only be true for a constant function.

But this would need a bit more explanation *why* constancy follows from that. And then its not that short anymore Wink

Website Find
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  The modified Bennet Operators, and their Abel functions JmsNxn 6 10,223 07/22/2022, 12:55 AM
Last Post: JmsNxn
  the inverse ackerman functions JmsNxn 3 16,714 09/18/2016, 11:02 AM
Last Post: Xorter
  generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 63,944 11/24/2011, 01:18 AM
Last Post: JmsNxn
  Would there be new insights if hyperops are extended to functions? Ivars 2 11,917 05/12/2008, 09:41 AM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)