Graph results of new number theory

The interesting part about my new number theory is the graphical representation of the results. When graphed one can see the similarity to the function y=1/x. There are a few exceptions, like being defined at x=0 now, and the fact that it approaches a finite or countable number of pieces on the x-axis and approaches the smallest measurable size on the y-axis. There are no irrational numbers generated and no negative cut can logically be made. We live in a finite world and nothing can be cut into an infinite amount of pieces therefore this new theory contradicts our current concept of infinity.