Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp
Ivars Wrote:3_log(a^b) =3_log(a[3]b)= 3_log(a)*3_log(b) = 3_log(a)[2]3_log(b)

This is where it starts to break down, because this is not a normal logarithm. Normal logarithms satisfy

Ivars Wrote:3_exp(a*b) =3_exp(a[2]b) = (3_exp(a))^(3_exp(b)) = 3_exp(a)[3]3_exp(b)

Since this is not the definition of logarithms, we should really separate out the 'log' notation from the equations:

Using these equations we can evaluate at the following points:

If :

then we find that f(a) is a constant.

If a=1:

then f(b) is a constant.

If b=1:

then we find the point f(1)=1.

If b=0:

which means f(a) is a constant.

So, not only can we show that f(x) is a constant, but we can show it in multiple ways, which is a very bad sign. I think this is proof that no such function can exist (or the only solution to all of these equations is f(x)=1).

Andrew Robbins

Messages In This Thread
RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by andydude - 06/02/2008, 04:46 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  The AB functions ! tommy1729 0 1,740 04/04/2017, 11:00 PM
Last Post: tommy1729
  the inverse ackerman functions JmsNxn 3 6,323 09/18/2016, 11:02 AM
Last Post: Xorter
  Look-alike functions. tommy1729 1 2,234 03/08/2016, 07:10 PM
Last Post: hixidom
  Inverse power tower functions tommy1729 0 2,030 01/04/2016, 12:03 PM
Last Post: tommy1729
  [2014] composition of 3 functions. tommy1729 0 1,920 08/25/2014, 12:08 AM
Last Post: tommy1729
  Intresting functions not ? tommy1729 4 5,500 03/05/2014, 06:49 PM
Last Post: razrushil
  generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 23,644 11/24/2011, 01:18 AM
Last Post: JmsNxn
  Discrete-analytic functions Ansus 4 6,057 07/30/2011, 04:46 PM
Last Post: tommy1729
  product functions tommy1729 5 6,830 06/01/2011, 05:38 PM
Last Post: tommy1729
  Periodic functions that are periodic not by addition JmsNxn 0 2,905 04/17/2011, 09:54 PM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)