{"product_id":"from-counting-numbers-to-complete-samuel-horelick-9781975629878","title":"From Counting Numbers to Complete Ordered Fields: Set-Theoretic Construction of","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Samuel Horelick\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1975629876\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781975629878\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Createspace Independent Publishing Platform\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/20\/2017\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 34\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.13lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.02h x 5.98w x 0.07d","brand":"Samuel Horelick","offers":[{"title":"Paperback","offer_id":43940432445695,"sku":"9781975629878","price":12.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_91a9400c-bdc8-45ea-b227-60dd830e21fc.jpg?v=1681447165","url":"https:\/\/www.whiterainbookhouse.com\/products\/from-counting-numbers-to-complete-samuel-horelick-9781975629878","provider":"WR Book House","version":"1.0","type":"link"}