Calendar · Lecture Notes
MIT OpenCourseWare
Paradox and Infinity
Art: Italian illuminator, Boethius initial consolation philosophy, 1385 · Public domain
- Instructor
- Prof. Agustín Rayo
- Term
- Spring 2019
- Level
- Undergraduate
- What's inside
- 8 problem sets · 22 lecture notes · 2 readings · 1 other file · 3 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 24.118 Paradox and Infinity, Spring 2019, Prof. Agustín Rayo — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.
Not included here
5 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (5 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Readings
Lecture Notes
21 files
- 24.118_S19 Paradox and Infinity, Lecture Note 1: The Cantorian Theory of Size I Download
- 24.118_S19 Paradox and Infinity, Lecture Note 2: The Cantorian Theory of Size II Download
- 24.118_S19 Paradox and Infinity, Lecture Note 3: The Ordinals I Download
- 24.118_S19 Paradox and Infinity, Lecture Note 4: The Ordinals II Download
- 24.118_S19 Paradox and Infinity, Lecture Note 5: Ordinals as Blueprints Download
- 24.118_S19 Paradox and Infinity, Lecture Note 6: Omega-sequence Paradoxes I Download
- 24.118_S19 Paradox and Infinity, Lecture Note 7: Omega-sequence Paradoxes II Download
- 24.118_S19 Paradox and Infinity, Lecture Note 8: Time Travel Download
- 24.118_S19 Paradox and Infinity, Lecture Note 9: Time Travel and Free Will Download
- 24.118_S19 Paradox and Infinity, Lecture Note 10: Newcomb's Problem Download
- 24.118_S19 Paradox and Infinity, Lecture Note 11: Probability, Subjective and Objective Download
- 24.118_S19 Paradox and Infinity, Lecture Note 12: Countable Additivity Download
- 24.118_S19 Paradox and Infinity, Lecture Note 13: Measure Theory Download
- 24.118_S19 Paradox and Infinity, Lecture Note 14: The Vitali Sets Download
- 24.118_S19 Paradox and Infinity, Lecture Note 15: Banach-Tarski: Preliminaries Download
- 24.118_S19 Paradox and Infinity, Lecture Note 16: Banach-Tarski: The Theorem Download
- 24.118_S19 Paradox and Infinity, Lecture Note 17: Computability: Turing Machines Download
- 24.118_S19 Paradox and Infinity, Lecture Note 19: Non-computable Functions II Download
- 24.118_S19 Paradox and Infinity, Lecture Note 20: Gödel's Theorem I Download
- 24.118_S19 Paradox and Infinity, Lecture Note 21: Gödel's Theorem II Download
- 24.119_S19 Paradox and Infinity, Lecture Note 18: Non-computable Functions I Download
Assignments
9 files
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 1: Infinite Cardinalities Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 2: The Higher Infinite Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 3: Omega-sequence Paradoxes Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 4: Time Travel Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 5: Newcomb's Problem Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 6: Probability Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Set 10: Gödel's Theorem Download
- 24.118_S19 Paradox and Infinity, Assignments: Problem Sets 7 and 8 Download
- 24.119_S19 Paradox and Infinity, Assignments: Problem Set 9: Computability Download
Course outline
Calendar · Lecture Notes
Lecture 2: Infinite Cardinalities (1)
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Lecture 3: Infinite Cardinalities (2)
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Lecture 4: Infinite Cardinalities (3)
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Lecture 5: The Higher Infinite (1)
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Lecture 6: The Higher Infinite (2)
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Lecture 7: The Higher Infinite (3)
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Lecture 8: Omega-Sequence Paradoxes (1)
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Lecture 9: Omega-Sequence Paradoxes (2)
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Lecture 10: Time Travel (1)
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Lecture 11: Time Travel (2)
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Lecture 12: Newcomb’s Problem (1)
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Lecture 13: Newcomb’s Problem (2)
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Lecture 14: Probability (1)
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Lecture 15: Probability (2)
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Lecture 16: Non-Measurable Sets (1)
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Lecture 17: Non-Measurable Sets (2)
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Lecture 18: The Banach-Tarski Theorem (1)
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Lecture 19: The Banach-Tarski Theorem (2)
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Lecture 20: Computability (1)
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Lecture 21: Computability (2)
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Lecture 22: Computability (3)
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Lecture 23: Gödel’s Theorem (1)
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Lecture 24: Gödel’s Theorem (2)
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Lecture 25: Review (1)
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Lecture 26: Review (2)
MIT OpenCourseWare, Prof. Agustín Rayo, 24.118 Paradox and Infinity, Spring 2019.
License: CC BY-NC-SA 4.0 · Edition: Spring 2019 · Open the original course on OCW ↗
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