Zeration reconsidered using plusation.
#1
X^^1 = x
X^1 = x
X*1 = x
X(+)1 = x

(+) is plusation.

It came to me that zeration ideas failed or were nonintresting because of using simple addition.

Therefore i now consider this plusation which is more logical.

X(+)2 = x + 1

For c real

X(+)(2^c) = x + c.

= x +1 (c times)

Notice x * 2^y = x + x (y times)

X ^ 2^y = x^2 (y times)

So plusation is a Natural logical operator in the list of noncommutative hyperoperators.

Plusation is like the superfunction of zeration.

Regards

Tommy1729
Reply
#2
It is not exactly the supefunction of zeration (max-kroenecker delta definition)...but it is the superfunction of Bennett's base 2 preaddition (-1th rank in base 2 commutative hos hierarchy).





In fact you are right: define plusation (set it as rank 1 of a new sequence)




Let's take it's subfunction in the variable x (i.e. where )




But the sequence doesn't seem much interesting or natural imho... the only nice properties are that
1) it is based on the usual recursion/iteration law (ML )
2) it intersects the 2-based commutative hos sequence at t=0 ()


MSE MphLee
Mother Law \((\sigma+1)0=\sigma (\sigma+1)\)
S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  Zeration GFR 92 196,571 06/30/2022, 11:47 PM
Last Post: MphLee
  Is this close to zeration ? tommy1729 0 4,271 03/30/2015, 11:34 PM
Last Post: tommy1729
  [2015] 4th Zeration from base change pentation tommy1729 5 12,852 03/29/2015, 05:47 PM
Last Post: tommy1729
  [2015] New zeration and matrix log ? tommy1729 1 6,648 03/24/2015, 07:07 AM
Last Post: marraco
  Zeration = inconsistant ? tommy1729 20 47,434 10/05/2014, 03:36 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)