Real numbers. the archimedes definition
The author of the article proposes a new definition of real numbers. The definition generalises the Eudoxus-Archimedes method of exhaustion and provides the uniform interpretation of such objects as real numbers, definite integrals and numeric methods for searching the roots of functions. The author discusses the advantages and limitations of the method and also gives a new definition of function continuity at a point, which agrees with the new real numbers definition.