If any local R member is also a global scale factor on the entire real-line and this duality recursively defines R members, then the real-line is a fractal as I show here:

1) As some unique number of the real line (a unique member of R set)

2) As a global scale factor on the entire real-line, which its product is the entire real-line included in itself according to this global scale.

There is no process here but a simultaneous existence of R set on infinitely many unique scale levels of itself.

Because of this self-similarity over scales, we can understand why some segment of the real line can have the magnitude of the entire real-line.

Please understand that we are not talking about some shape of a fractal, but on the infinitely many levels of non-empty elements, which are included in R set.

It is important to stress that there is one and only one magnitude to the real line, which is not affected by its fractal nature.

1. You've not explained what global scale factor means, just used the words again.
2. if fractals have nothing to do with it why do you keep banging on about them
3. R is an infinite set, that is all youy're saying
4. magnitude has not been defined properly, given your weird views on cardinality and lack of understanding of the usage of words in proper mathematics youy should at least try to explain what you mean, though you will fail almost surely.