Up to the next line
We notate the 0th dimension.
We have a line that is composed of 0-dimensional dots, so we will note the number of dots with n=n dots.
Up to the next plane
We notate the 1st dimension.
The limit of the first line will be notated as X. And dots in the next line will be denoted as X+n.
We have a plane that is composed of 1-dimensional lines, so we will note the number of lines with mX=m lines.
So for m lines and n dots on the m+1th line, we have mX+n.
Up to the next cube
We notate the 2nd dimension.
The limit of the first plane will be notated as X2. And dots+lines in the next plane will be denoted as X2+mX+n.
We have a cube that is composed of 2-dimensional planes, so we will note the number of planes with lX2=l planes.
So for l planes and m lines in the l+1th plane and n dots on the m+1th line in the l+1th plane, we have lX2+mX+n.
Up to infinite number of dimensions.
n describes the number of dots in the next line.
mX describes the number of lines in the next plane.
lX2 describes the number of planes in the next cube.
And basically, aXb describes the number of b-dimensional spaces in the next b+1-dimensional space.
We have exponentiation of X to a natural number. How about exponentiation of X to a polynomial?
We have XX as the next hyperdimension. Hyperdimensions are types of dimensions beyond normal dimensions, which are used to describe dimensions.