portada From Counting Numbers to Complete Ordered Fields: Set-Theoretic Construction of (en Inglés)

From Counting Numbers to Complete Ordered Fields: Set-Theoretic Construction of (en Inglés)

Formato

Libro Físico

Autor

Samuel Horelick

Editorial

Createspace

Idioma

Inglés

N° páginas

Encuadernación

Tapa Blanda

Dimensiones

22.9x15.2x0.2 cm

Peso

0.06 kg.

ISBN13

9781975629878

Categorías

Teoría de los conjuntos

From Counting Numbers to Complete Ordered Fields: Set-Theoretic Construction of (en Inglés)

Samuel Horelick (Autor) · Createspace · Tapa Blanda

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Reseña del libro "From Counting Numbers to Complete Ordered Fields: Set-Theoretic Construction of (en Inglés)"

This paper present set-theoretic construction of number sets beginning with von Neumann definition of Natural numbers. Integers are defined in terms of Natural numbers. The set of integers Z is defined to be the set of equivalence classes of ordered pairs (x, y) where x, y are Natural numbers. Integers form a Commutative Ring with Unity. The set of Rational numbers Q is defined to be the set of equivalence classes of ordered pairs (x, y) where x, y are Integers. Rational Numbers form a Field. Rational and Irrational numbers. Dedekind cut. Real numbers form Complete Ordered Field. Further topics include Countable and Uncountable sets, Finite and Infinite sets, the sizes of Infinities, Countable Rational and Uncountable Real numbers, Power Set, Cantor's theorem, Cantor's Paradox, Russell's paradox, Zermelo axioms for set theory, Essentials of Axiomatic method, Continuum Hypotheses, Unlimited Abstraction Principle and Separation Principle, Undecidability of Continuum Hypotheses in Zermelo-Fraenkel system, objections to Zermelo system, and other topics. The paper is aimed at Mathematics and Theoretical Computer Science students.