The aim of the paper is to define mathematics concepts and the interaction between them based on the unified framework of mathematics by the philosophy method proposed in “Map of Mathematics under Yin-Yang Theory”. Firstly, develop & prove addition, subtraction, multiplication & division with the help of “form” & ‘equation’; then define negative number with the help of the concept of opposite unit interval (-). After these efforts, the activity of proving commutative property of addition & multiplication is conducted. Next goals are to define continues number with the help of arrays of assembly of unit intervals and refine the definition of ‘epsilon-delta’ limit with the help of the newly defined continuity concept. Then refine definition of 1D, 2D & 3D space; from the introduced space, refine the definition of vector & combination of vectors. Lastly. explore the interaction between concepts of variable, limit, space & origin by the concept of graph and derivative.
Keywords: Limit, arithmetic concepts, commutative properties of addition & multiplication, mathematics framework, negative number, space
