Tetration Forum
Zeration reconsidered using plusation. - Printable Version

+- Tetration Forum (https://math.eretrandre.org/tetrationforum)
+-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)
+--- Thread: Zeration reconsidered using plusation. (/showthread.php?tid=1008)



Zeration reconsidered using plusation. - tommy1729 - 05/29/2015

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


RE: Zeration reconsidered using plusation. - MphLee - 10/23/2015

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 ()