• Home
  • TI-84 Tutorials
  • How to Convert HW to a PDF File
  • Graph Paper
  • M105 at IUK
    • TI-84 Tutorials
    • Semester Schedule & M105 At A Glance
    • Course Syllabus & Lecture Content List
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 4
    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • AP Calculus AB at THS
    • Calculus Class Pictures
    • Calculus Student Inventory
    • TI-84 Tutorials
    • Zoom Meeting Recordings
    • Monthly Calendars
    • Web Assignments
    • AP College Board YouTube
    • AP Calculus AB Exam
    • ACP Calculus - IU
    • Memorization Sheets
    • Calculus Memorization Quizzes
    • Test/Quiz Correction Analysis
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Last Chapter/Review
    • Final Exam Review WS
    • The Calculus Life Saver
    • Final Calculus Video Project
    • Past AP Calculus AB Scores
  • Pre-Calculus (H) at THS
    • TI-84 Tutorials
    • Monthly Calendars
    • Pre-Calculus Student Inventory
    • Trig Memorization Quizzes
    • Web Logs >
      • Web Log #1
      • Web Log #2
      • Web Log #3
      • Web Log #4
      • Web Log #5
      • Web Log #6
      • Web Log #7
      • Web Log #8
      • Web Log #9
      • Web Log #10
      • Web Log #11
      • Web Logs #12 - 17
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 8
    • Chapter 7
    • Final Exam Study Guides
    • Regression Project
    • Are You Ready for Calculus? >
      • Independent Calculus Preparation
      • ETSU Calculus I Readiness Assessment
      • University of California Calculus Readiness Test
      • Sample Mathematics Placement Exam
      • Paper & Pencil Practice Exams
  • Pre-Calculus (R) at THS
    • TI-84 Tutorials
    • Pre-Calculus Student Inventory
    • Monthly Calendars
    • Zoom Meeting Recordings
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 10
    • Projects >
      • Math Goes To The Movies
      • Curve Project Screencast
      • Topic Screencast
      • Let The Artist in You Shine! Project
      • Mathematician Presentation Using Google Slides
      • Which Mathematician Was Born on Your Birthday? Project
      • Parabola Project Using Desmos
      • Regression Project
      • Programming the TI-84 Project
      • Law of Sines & Law of Cosines Diorama Project
      • Trigonometry Goes To The Movies A Poster Project
  • Exit Ticket
  • Calculator Recommendation
  • Cole's World of Mathematics Disclaimer
    • Cole's World of Mathematics Privacy Policy
COLE'S WORLD OF MATHEMATICS
  • Home
  • TI-84 Tutorials
  • How to Convert HW to a PDF File
  • Graph Paper
  • M105 at IUK
    • TI-84 Tutorials
    • Semester Schedule & M105 At A Glance
    • Course Syllabus & Lecture Content List
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 4
    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • AP Calculus AB at THS
    • Calculus Class Pictures
    • Calculus Student Inventory
    • TI-84 Tutorials
    • Zoom Meeting Recordings
    • Monthly Calendars
    • Web Assignments
    • AP College Board YouTube
    • AP Calculus AB Exam
    • ACP Calculus - IU
    • Memorization Sheets
    • Calculus Memorization Quizzes
    • Test/Quiz Correction Analysis
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Last Chapter/Review
    • Final Exam Review WS
    • The Calculus Life Saver
    • Final Calculus Video Project
    • Past AP Calculus AB Scores
  • Pre-Calculus (H) at THS
    • TI-84 Tutorials
    • Monthly Calendars
    • Pre-Calculus Student Inventory
    • Trig Memorization Quizzes
    • Web Logs >
      • Web Log #1
      • Web Log #2
      • Web Log #3
      • Web Log #4
      • Web Log #5
      • Web Log #6
      • Web Log #7
      • Web Log #8
      • Web Log #9
      • Web Log #10
      • Web Log #11
      • Web Logs #12 - 17
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 8
    • Chapter 7
    • Final Exam Study Guides
    • Regression Project
    • Are You Ready for Calculus? >
      • Independent Calculus Preparation
      • ETSU Calculus I Readiness Assessment
      • University of California Calculus Readiness Test
      • Sample Mathematics Placement Exam
      • Paper & Pencil Practice Exams
  • Pre-Calculus (R) at THS
    • TI-84 Tutorials
    • Pre-Calculus Student Inventory
    • Monthly Calendars
    • Zoom Meeting Recordings
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 10
    • Projects >
      • Math Goes To The Movies
      • Curve Project Screencast
      • Topic Screencast
      • Let The Artist in You Shine! Project
      • Mathematician Presentation Using Google Slides
      • Which Mathematician Was Born on Your Birthday? Project
      • Parabola Project Using Desmos
      • Regression Project
      • Programming the TI-84 Project
      • Law of Sines & Law of Cosines Diorama Project
      • Trigonometry Goes To The Movies A Poster Project
  • Exit Ticket
  • Calculator Recommendation
  • Cole's World of Mathematics Disclaimer
    • Cole's World of Mathematics Privacy Policy
COLE'S WORLD OF MATHEMATICS
Set Theory Unit
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.  Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.  
Picture
Georg Cantor (1845 - 1918)
A single paper written in 1874 by Georg Cantor founded the modern study of set theory.  The paper was called “On a Property of the Collection of All Real Algebraic Numbers”.  The next wave of excitement in set theory came around 1900, when it was discovered that some interpretations of Cantor’s work on set theory gave rise to several contradictions, called paradoxes.  Fortunately, the debate surrounding the paradoxes in Cantor’s set theory did not lead to its abandonment.  Instead, the work of Ernst Zermelo and Abraham Fraenkel resulted in a set of axioms in order to formulate a theory of sets free of paradoxes such as the paradoxes found in Cantor’s work.

Lecture Notes & Other Resources
TENTATIVE SCHEDULE FOR THE UNIT

Set Theory - Day 1
Introduction to Set Theory (Elements, Empty Set, Finite & Infinite Sets, Subsets & Proper Subsets, and the Correct Notation).

-----VIDEO: What are Sets?
-----VIDEO: Sets - Listing Method (or Roster Method)
-----VIDEO: How Do We Write Long Lists of Elements?
-----VIDEO: How Do We Represent Sets? Set Builder Notation & Venn Diagrams
-----VIDEO: How Do We Name A Set?
-----VIDEO: Can Elements in a Set Be Repeated?
-----VIDEO: Finite and Infinite Sets
-----VIDEO: What are Singleton and Empty Sets?
-----VIDEO: What is a Subset?
-----VIDEO: Subsets, Proper Subsets, and Supersets
-----VIDEO: Null Set - Is it a Subset of Every Set?

VIDEO: Cantor's Infinity Paradox

Set Theory - Day 2
Unions, Intersections, Complements, and the Universal Set

-----VIDEO: What is a Universal Set?

Set Theory - Day 3
Venn Diagrams

-----VIDEO: What is a Venn Diagram?
-----VIDEO: How Do We Understand Union and Intersection Using Venn Diagrams?
-----VIDEO: How Do We Visualize Different Regions in Venn Diagrams?
-----VIDEO: How Do We Visualize Regions in a 3 Set Venn Diagram?

Set Theory - Day 4
Cardinality and Cardinality Properties

-----VIDEO: What is a Cardinal Number?
-----VIDEO: What are Equivalent Sets?
-----VIDEO: Equal and Equivalent Sets

Set Theory Unit Project

A Combined Google Form Assessment for the Graph Theory and Set Theory Units

Picture
Copyright © 2013-21
​Cole's World of Mathematics.
ALL RIGHTS RESERVED.
Picture
Picture