Schedule

• Test 4 will be in class on Wednesday, 23 April. Preparation Guide for Test 4

Class

• Finishing Proof of Cantor’s Theorem
• Review for Test 4

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Test 4 will be in class on Wednesday, 23 April.

Class

• Uncountability of the Real Numbers
• Cantor’s Theorem
• Proving Cantor’s Theorem

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Problem Set 8 is now posted and is due before 8:29pm on Thursday, 17 April: [PDF] [Template]
• Test 4 will be in class on Wednesday, 23 April.

Class

• Review: Proving Uncountability
• Infinite Binary Strings (recap)
• \( \pow(\mathbb{N}) \)
• Python programs
• Real numbers

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Problem Set 8 is now posted and is due before 8:29pm on Thursday, 17 April: [PDF] [Template]

Class

• Explaining the Rest of the Semester
• Proofs of Uncountability
• Diagonalization Proofs
• Cantor’s Diagonalization Proof (1891)

For the story behind the book and high quality scan, see Cantor’s (No Longer) Lost Proof.

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Problem Set 8 is now posted and is due before 8:29pm on Thursday, 17 April: [PDF] [Template]

Class

• Potential and Actual Infinities
• Cantor vs. Aristotle, Aristotle, Kronecker, Poincaré, St. Thomas Aquinas, Pope Leo XIII, etc.
• English is a Disaster
• Definiting Infinite, Countable, Uncountable, Countably Infinite
• Proofs of Countability and Uncountability

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Problem Set 7 is due before 8:29pm on Thursday, 10 April: [PDF] [Template]

Class

• \( \mathbb{N} \times \mathbb{N} \) and \( \mathbb{Q} \) are Countably Infinite
• Binary Strings
• Uncountably Infinite

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Problem Set 7 is due before 8:29pm on Thursday, 10 April: [PDF] [Template]

Class

• Defining Infinite and Countable Sets
• Review of Binary Relations
• All Finite Sets are Countable
• The Integers are Countably Infinite

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Problem Set 7 is now posted and is due before 8:29pm on Thursday, 10 April: [PDF] [Template]

Class

• Defining Infinite Sets
• Cardinality of infinite sets
• Countable Sets

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Test 3 will be in class on Wednesday, 2 April. See the Preparation Guide for Test 3 for practice problems, and send me a DM for any topics or problems you want covered in the review class on Monday.
• The TAs will hold a review session today (Monday), 5:00-6:30pm in Olsson 009.

Class

• Review for Test 3
• Practice Problems
• Flavors of Induction

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]

Schedule

• Test 3 will be in class on Wednesday, 2 April. See the Preparation Guide for Test 3 for practice problems, and send me a DM for any topics or problems you want covered in the review class on Monday.

Class

• Proofs using stronger induction
• Winning the Takeaway game

10am Section: [Slides (PDF)] [Video]
2pm Section: [Slides (PDF)] [Video]