Since axiom 1 is illogical, it is meaningless to say that the given line segment consists of a finite number of zeros, and furthermore, since axiom 3 is logical, it is also meaningless to say that it consists of an infinite number of zeros. Consequently, the concept that a given line segment can be divided infinitely into smaller parts is replaced by the concept of the change in direction indicating one quantitative continuum in axiom 3 where any given line segment is the quantitative continuum itself. Of course, this any given line segment is also nonexistent because if we assume that it exists, then the comparison with other quantities relative to it will be given the meaning of being able to compare the size, which obviously comes into the dilemma of acknowledging the third axiom.