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Paradox and Infinity
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Introduction
About this Class
How to use this website
Acknowledgments
Infinite Cardinalities
Introduction
Hilbert's Hotel
Size Comparisons
The Real Numbers
Cantor's Theorem
The Power Set of Natural Numbers
Summary and Further Resources
Homework (9 Questions)
This content is graded
The Higher Infinite
Introduction
The Higher Infinite
Ordinals
Ordinal Arithmetic
Ordinals as Blueprints
Paradox
Summary and Further Resources
Homework (6 Questions)
This content is graded
Omega-Sequence Paradoxes
Introduction
Omega-Sequence Paradoxes
Rational Decision-Making
Reverse Omega-Sequence Paradoxes
Hat-Problems
Summary and Further Resources
[Bonus: Meet the Experts]
Homework (4 Questions)
This content is graded
Time Travel
Introduction
Time Travel
Time Travel and Physical Law
Free Will
Summary and Further Resources
[Bonus: Meet the Expert]
Homework (4 Questions)
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Newcomb's Problem
Introduction
The Problem
Maximizing Expected Value
In Defense of Two-Boxing
Causal Decision Theory
Summary and Further Resources
[Appendix: The Prisoner's Dilemma]
[Appendix: The Tickle Defense]
Homework (4 Questions)
This content is graded
Probability
Introduction
Probability, Subjective, and Objective
Subjective Probability
Objective Probability
The Principle of Countable Additivity
[Optional: The Two-Envelope Paradox]
Further Resources
[Bonus: Meet the Expert]
Homework (4 Questions)
This content is graded
Non-Measurable Sets
Introduction
Measures
Non-Measurable Sets
Summary and Further Resources
Homework (5 Questions)
This content is graded
The Banach-Tarski Theorem
Introduction
The Banach-Tarski Theorem: Three Warm-Up Cases
The Theorem
Summary and Further Resources
Computability
Introduction
Turing Machines
Non-computable functions
Efficiency
[Optional: The Big Number Duel]
Summary and Further Resources
[Bonus: Meet the Expert]
Homework (5 Questions)
This content is graded
Godel's Theorem
Introduction
Godel's Theorem
A Proof of Godel's Theorem
The Philosophical Significance of Godel's Theorem
Summary and Further Resources
[Appendix: Proof of the Lemma]
Homework (4 Questions)
This content is graded
Glossary
Symbols and Concepts