A geometry consisting of singularities containing only integers

Abstract It is difficult for us to discriminate the sizes of space and time as finite and infinite. In this article an axiom is defined in which one infinitely small and infinitely great must exist if the sizes of space and time can be compared and it is undividedly 0(zero) point (singularity) for this infinitely small.this axiom have some new characters distinct from current calculus ,such as extension only can be executed in the way of unit superposition in the system, the decimal point is meaningless and there aree only integers to exist in the system, and any given interval is finite quantites and can not be ‘included’ or ‘equal divided’ infinitely and randomly.The geometry space we see are the non-continuum being made of countless 0 points .