Equivalent Sets and Cardinal Numbers

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Description

The purpose of this thesis is to study the equivalence relation between sets A and B: A o B if and only if there exists a one to one function f from A onto B. In Chapter I, some of the fundamental properties of the equivalence relation are derived. Certain basic results on countable and uncountable sets are given. In Chapter II, a number of theorems on equivalent sets are proved and Dedekind's definitions of finite and infinite are compared with the ordinary concepts of finite and infinite. The Bernstein Theorem is studied and three different proofs of it are ... continued below

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38 leaves

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Hsueh, Shawing December 1975.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 225 times , with 27 in the last month . More information about this thesis can be viewed below.

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  • Hsueh, Shawing

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Description

The purpose of this thesis is to study the equivalence relation between sets A and B: A o B if and only if there exists a one to one function f from A onto B. In Chapter I, some of the fundamental properties of the equivalence relation are derived. Certain basic results on countable and uncountable sets are given. In Chapter II, a number of theorems on equivalent sets are proved and Dedekind's definitions of finite and infinite are compared with the ordinary concepts of finite and infinite. The Bernstein Theorem is studied and three different proofs of it are given. In Chapter III, the concept of cardinal number is introduced by means of two axioms of A. Tarski, and some fundamental theorems on cardinal arithmetic are proved.

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38 leaves

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  • December 1975

Added to The UNT Digital Library

  • June 24, 2015, 9:39 a.m.

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  • July 26, 2016, 9:18 a.m.

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Hsueh, Shawing. Equivalent Sets and Cardinal Numbers, thesis, December 1975; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc663009/: accessed October 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .