There is a line segment.
The line segment is composed of infinite line segments, which in turn are composed of infinite line segments;
The line segment composes infinite line segments, with each line segment composed infinite line segments.
The level of division of the line segment retains the division as the line segment itself across scale as the line segment being the degree by which the line segments are divided as line segments.
Division requires that which divides, the limit of division is that which divides thus resulting in division as self-scaling of what is dividing within the context of that which is divided.
Division as self scaling inversely result in magnification of what is dividing for a line segment X which contains line segments Y is effectively Y repeated multiplicatively as the whole line segment X as scale.
Division and multiplication are inverses, these inverses are fractal states unfolding by degree of compression (division) and expansion (multiplication).
What remains is scale invariance as the fixed point of division or multiplication resulting in scales; a line segment as two line segments is the one as a ratio of itself, two line segments as one line segment is the two as the ratio itself.
Division and Multiplication are fractal in nature; they are inverse aspects of recursive scaling.