Abstract

The various numerical classes are determined on the base of set theory concepts. The natural numbers are cardinalities of finite sets. Using addition and multiplication of cardinalities, subsequent classes of numbers are definite. Particularly, the integer, rational, and algebraic numbers are solutions of additive, multiplicative, and algebraic equations respectively. The real numbers can be determined as cuts of the set of rational numbers. The complex numbers and its extensions are tuples of real numbers. The numerical classes turn out to be the most beautiful models of all kinds of mathematical objects that occur along our path. Based on certain properties of specific numerical sets, we come to different types of mathematical structures.

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