A new definition of our number line.
In classic education, our number line is defined as a line that extends infinitely from minus infinity to plus infinity.
Within this line, a section is divided infinitely, to give another number line that extends infinitely from minus infinity to plus infinity.
Within this line, a section is further divided infinitely, to give another number line that extends infinitely from minus infinity to plus infinity, and so on.
This serves no purpose except to define nothing with nothing.
A number line should only represent integer values, since values that have no exact value, such as root two or pi, can only ever be given an approximate value represented by integer numbers.