New Choice of the Primitive Concept of Mathematics

In this paper,element is selected as primitive concept of mathematics.The element needs to satisfy 5 postulates defined,so that element is a basic, unified,independent,definite and clearly demarcated object,on which to base sequence and set from elements.Moreover,5 axioms of set`s constructing are defined: The empty is the initial point of the set and its successor is checked;The successor can be arranged in the array.The termination of arranging can just end the set.The successor can exist forever in reality.The infinite successor can be ended in ideal.Meanwhile,new definition of infinite set is defined: The set,the arranging of its elements without one being leaked in the ideal and have successors forever in reality.The infinite sequence is used to reflect the infinite's process and the infinite set is used to reflect the infinite's termination.The two above-mentioned are not obscure.5 axioms of the natural number sequence-set formulation are defined newly: The 0 is the lower bound;The 1 is the basic order;The n is standard quantity;The w is infinite successor;The ∞ is the upper bound.The measurement of number and the termination of infinite should be reflected in our axiom.Studying philosophy of mathematics and constructing foundation of mathematics are connected closely,it is hoped to make a try to 3 groups of postulates and axioms be clear logic relations and concise graceful forms.