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 has 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 are only integers to exist in the system, and any given interval is finite quantities and cannot be ‘included’ or ‘equal divided’ infinitely and randomly. The geometry space we see is the non-continuum being made of countless 0 points.