Even though other sets of numbers can function much like a set of integers does, in formulating the desired output. However, we look closer on all the possible outcomes generated for all values where x is an element of integers. Not including zero for special circumstances, since length does not equal to zero. Whereas for certain circumstances where zero holds, a set of real numbers is preferred much as other values hold. Thus, holding such a system fixed; for transformation of all the objects in question to yield contractions and expansions as x increases or decreases by 1. Unless such functions alter their cause as a result of an introduction of asymptotes into a set of an entire collection of objects whose properties are under investigation.

Keywords: Algebra, Geometry, Analysis, Functions