Set Theory Unit
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
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

