Based on OOP construction, numbers, for example, can be constructed differently. Different constructions may contain new properties and view numbers from a different perspective.
It was said that natural numbers (or n+1 algorithm) never reach infinity. Because, for some finite number n, n+1 is also a finite value. Real numbers never reach infinity as well. However, it was discussed previously that projective geometry adds an inf mechanism to R. The same is true for N. It means it’s possible to add an inf mechanism to N as well. If natural numbers are placed on a line (to form a lattice), the distance between consecutive elements is always 1. Still, when viewed by the stationary observer located at the origin, the growth rate shrinks. That is (n+1)/n approaches 1 at infinity.
The next section of the inf article discusses an inf mechanism for N. The approach is to consider 1 (the step size) and n as distinct entities. Then It’s possible to assign different behaviours to 1 and n. This is necessary because 1 gradually tends to zero, and the motion of n stops at inf. This can be done by utilizing the circular symmetry. This will be explained in more detail later on but briefly, n+1 is always a point on the complex unit circle, the step size is the cosine and n is the sine. Based on this approach natural numbers are described based on a new symmetry and the aim is to see if it provides new info about N.
New symmetries may shed light on previously undetected properties. This is also true in the social context. For example, if the symmetry of a government (i.e. a system) is based on military purposes, these purposes define foreign, economic, etc. mechanisms and relations. The aim should be to change the symmetry so that the defining element of a system moves away from military purposes (for example) to economic processes.