Development of the number system

Abstract

There is no occupation in which a man would not have to perform simple calculations. The numbers used in such tasks are a means of grasping and mastering the world quantitatively. But statements of general validity can be based on arithmetical operations only when the laws underlying the calculations are known. The accumulated experience of millionfold applications in the historical development of mankind is laid down in computational rules that can be reduced to a few logical fundamental concepts and axioms. The foundations for this deductive build-up of the number system are the theory of sets and mathematical logic. On this basis first the natural numbers, and then the further domains of numbers, are constructed.