Ternary Mathematics and 3D Placement of Logical Elements Justification

The research presented in the following application aims to prove use of Ternary Maths for calculating machines and to simplify the process of calculating In it we will try to justify the use of triplets and describe how it works. An earlier research presented in “Logical Principles in Ternary Mathematics” [1,2,3] shows that we can transit from one expression of a number such as a "component form" to another, e.g a decimal, or still another, that is it’s vector form [4]. The aim of our further research is to explain why we associate Triplets of numbers in such choice {-1,0,1} and not the numbers 1,2,3 for example, or a set {1,2,3} The explanation seems obvious as a set of decimal numbers consists of 10 entries not 3 At the same time we have to prove that the mentioned set of triplets is a unique and the only one to be used as a Ternary Set or a base, as we might call it, for our calculating machines