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Set-Theoretic Paradoxes and their Resolution in Z-F
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Countable/Uncountable sets, Sizes of Infinity, "Hilbert Hotels", Power set, Cantor’s theorem and Paradox, Russell’s paradox, Zermelo's axioms for set theory, Essentials of Axiomatic method, Continuum Hypotheses, Unlimited Abstraction Principle and Separation Principle, Undecidability of Continuum Hypotheses in Zermelo-Fraenkel system, Note on the objections to Zermelo’s system.
Author
Samuel Horelick
Dr. Samuel Horelick is mathematics professor and educational consultant. He has graduated from three Universities with four degrees: in Mathematics, Philosophy, Mathematical Education, and Theology
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Set-Theoretic Paradoxes and their Resolution in Z-F - Samuel Horelick
FAMOUS SET–THEORETIC PARADOXES, AND THEIR RESOLUTION IN ZF
By Samuel Horelick
Smashwords Edition – Published by Smashwords
Copyright © 2012 by Samuel Horelick. All rights reserved.
Contents:
1. Countable/Uncountable sets
2. Finite/Infinite sets
3. Hilbert Hotel
examples
4. Smaller/larger sets and the sizes of Infinity
5. Countable Rational and Uncountable Real numbers: proofs
6. Power set
7. Cantor’s theorem, Cantor’s Paradox, and Russell’s paradox
8. Zermelo's axioms for set theory
9. Essentials of Axiomatic method
10. Continuum Hypotheses revisited
11. Unlimited Abstraction Principle and Separation Principle
12. Undecidability of Continuum Hypotheses in Zermelo-Fraenkel system
13. Note on the objections to Zermelo’s system.
How to decide if two sets are of the same size without the appeal to a concept of size
?
Well, if we could find a way to assign an element of one set to an element of the other set so that each element of one set is assigned to exactly one, unique element of another
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