 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 ()