Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
between addition and multiplication
#17
This is fucking beautiful! I've been working at this for three years now and you beat me to the punch! LOL!

Do you have a closed form expression for it yet? I have so many ideas involving rational operators.

And one thing that MUST be true is

x {1.5} 2 = x {0.5} x

If that's not true then the system doesn't meet requirements. But it wouldn't be hard to improvise a system since 0 <= q <= 1, {q} is defined.

Also, I wonder if we could try to implement the laws of logarithmic semi operators into this system:

q:log(x) = exp^[-q](x)

q:log(x {q} y) = q:log(x) + q:log(y)
q:log(x {1+q} y) = q:log(x) * y

And if we implement this we can feasibly solve for a new variation of tetration.

Since
x {0.5} y = arithmetic/geometric limiting algo
= -0.5:log(0.5:log(x) + 0.5:log(y))
= sexp(slog(sexp(slog(x)-0.5) + sexp(slog(y)-0.5)) + 0.5)

Holy jesus, yes!

And also, I was wondering what our identities are?, if S(q) is the identity function and x {q} S(q) = x, S(1) = 1, and S(0) = 0 obvi, but what is S(q)?

I found S(0.5) = 0.7019920407 for 2 {0.5} S(0.5) = 2. I used 1000 cycles so my numbers are probably more accurate.
However, sadly, S(0.5) for 3 {0.5} S(0.5) = 3 is a different number and therefore {q} has no identity. This is very sad indeed.
Reply


Messages In This Thread
between addition and multiplication - by lloyd - 03/10/2011, 09:10 PM
RE: between addition and multiplication - by JmsNxn - 03/15/2011, 06:11 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,887 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Between addition and product ( pic ) tommy1729 4 3,755 07/10/2016, 07:32 AM
Last Post: Gottfried
  special addition tommy1729 0 1,791 01/11/2015, 02:00 AM
Last Post: tommy1729
  extension of the Ackermann function to operators less than addition JmsNxn 2 4,020 11/06/2011, 08:06 PM
Last Post: JmsNxn
  Periodic functions that are periodic not by addition JmsNxn 0 2,731 04/17/2011, 09:54 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)