Figure 2 (1) With stationary Cartesian coordinates, 3×108 meters is equivalent to 1 second, and the time beat is given as 1 second (= 3×108 meters). (2) For Cartesian coordinates with a velocity of 3 m/s, 3×108 × 1/(1-3/c)meters is equivalent to 1×1/(1-3/c)seconds, with the time beat given as  1/(1-3/c)seconds  (= 3×180 ×1/(1-3/c) meters). It is concluded from relativity that a velocity of 3 m/s will be given in the form of 3×180 ×1/(1-3/c) meters  /  1×1/(1-3/c)seconds .
 
 
4 Principle of an inertial system and the principle of universal invariant velocity for Axiom 1
 
Principle of an inertial system for Axiom 1 It is known from Axiom 1 that relativity is not true. As shown in Figure 3, in Axiom 1, each inertial system is described by a unit value, such as 2, 3, or 4. In this system, the properties of the proportional extension of two inertial frames can then be considered. For example, two inertial frames 2 () 1 are compared, with the following extension ratios being 4 (), 2, 6 (), 3, 8 (), 4, etc. In this comparison of inertial frames, we also consider a unit extension of 4 () 2 to the same ratio, meaning the next extension ratio is 8 () 4, followed by 12 () 6, and so on. Comparing 8 () 4 to the same scale unit extension, the next is 16 () 8, followed by 24 () 16, and so on. Although the ratio is 2/1, the two units extend differently and cannot replace or offset each other because of the different units (the former is in units of 4 and the latter is in units of 8). Therefore, relative velocity is meaningless in Axiom 1, which means that a given quantity, as distinct from the other units of quantity, can only be itself and not any other quantity; this particular quantity thus represents only one state, not any other state, and the Cartesian coordinate system does not apply in Axiom 1. As a result, the properties of the inertial system of relativity need to be revised.
First, in the principle of an inertial system for Axiom 1, an inertial system is a specific quantity and only represents a state, so the motion of all quantities is absolute, and any comparison of the motion of two quantities is also absolute.
Second, the absoluteness of this motion negates the relativity principle of relativity theory. Thus, it can be said that a stationary concept is also meaningless in the principle of an inertial system for Axiom 1. In the principle of relativity, if K is a stationary Cartesian inertial system (i.e., the coordinates for all space and time variables are stationary relative to K), K’ is a moving Cartesian inertial system relative to K with velocity v so, following the Axiom 1 inertial system principle, it is meaningless to talk about all space-time variables as stationary relative to K', and K does not exist as an inertial system at rest. It can thus be said that the Cartesian coordinate system cannot describe the distribution of quantities in space and time and that all-embracing variables in space and time that stand stationary relative to the coordinate system do not exist.
Thirdly, unlike the coordinate system, which must be described with two different terms as discussed above, the inertial system in Axiom 1 only has a quantitative term description, such as an inertial system whose space units are 1, 4, 8, or N (all are multiples of 0). An inertial frame represents only a specific quantity, that is, only a state.
Fourth, consider the comparison of two inertial systems in Axiom 1, such as the 4()1 proportionate extension, where inertial system 4 extends in units of 4, and inertial system 1 extends in units of 1. The extension of the two inertial systems involves an infinite number of different comparisons except that the extension ratio of 4:1 is fixed. For example, the extension of inertial system 4 is 4, 8, 12, 16, etc. (infinitely many different quantities), while the extension of inertial system 1 is 1, 2, 3, 4, etc. (infinitely many different quantities). Thus, the difference between the two inertial systems is not a difference of one quantity, but an infinite number of quantities.
The Cartesian coordinate system which thus describes the difference in a quantity cannot be applied to describe infinitely many differences. In addition, in a Cartesian coordinate system moving with velocity v, all of the points moving with velocity v are meaningless because, in Axiom 1, point 0 only represents point 0 and cannot be endowed with other concepts, such as point 0 moving with a velocity that is two-dimensional.