Hassan Sedaghat
Abstract
Abstract The real numbers are constructed from the rational numbers using Cantor’s approach (important material often omitted from introductory textbooks in real analysis). The fundamental properties of real numbers, like completeness, the density of rationals, the least upper bound property, and the Bolzano-Weierstrass theorem are stated and proved.
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Abstract The real numbers are constructed from the rational numbers using Cantor’s approach (important material often omitted from introductory textbooks in real analysis). The fundamental properties of real numbers, like completeness, the density of rationals, the least upper bound property, and the Bolzano-Weierstrass theorem are stated and proved.
Key concepts: Rational number, Real number, Mathematics, Completeness (order theory), Property (philosophy), Real analysis, Discrete mathematics, Arithmetic