Refined Definitions in Real Numbers and Vectors and Proof of Field Theories

摘要

A set of new and refined principles and definitions in Real Numbers and Vectors are presented. What is a Vector? What is the meaning of the Addition of two Vectors? What is a Real Number? What is the meaning of their signs? What is the meaning of the Addition of two Real Numbers? What is the Summation Principle in Addition Operation? What is the Cancellation Principle in Addition Operation? What is the Meaning of the Multiplication of two Real Numbers? Is Field Theory a law? Can it be proved? All these issues are addressed in this paper. With better pictures and graphical presentations, proof of Field Theories in Real Numbers and Vectors including Commutativity, Associativity and Distributivity are also proposed.