xelpmoC function

First I define ${\mathbb {X}}$ as the union of every algebra produced by the Cayley-Dickson construction.

Then, xelpmoC(m,n) for any m$\in {\mathbb {X}}$ and non-negative integer n is defined as follows:

xelpmoC(m,0) = 1

xelpmoC(m,n+1) = xelpmoC(n)^m+$i_n$ where $i_n$ is the n-th imaginary unit.

Another function whose domain is the non-negative integers and whose range is the elements of ${\mathbb {X}}$:

complexsum(1) = 1

complexsum(n+1) = complexsum(n)+$i_n$ where $i_n$ is the n-th imaginary unit of the algebra which has an n-th imaginary unit produced by the fewest number of Cayley-Dickson constructions .

I define Imaginary Boundless Constant as $\lim_{n\rightarrow\infty}$complexsum(n)

Should Imaginary Boundless Constant be considered an infinite number?