Proof Index
TOC
Courses
Subreddit
Blog
Search
▾
Naive set theory
•
Set operations
•
Basic set theory proofs using Venn diagrams
•
Basic set theory proofs using membership tables
▸
Basic set theory proofs using predicate logic
•
Proof: Symmetric difference is associative
•
Basic set theory proofs using set identities
•
Cardinality from Venn diagrams
▸
Cardinality of power set of finite set
•
Proof by induction: Cardinality of power set of finite set
•
Proof using binomial theorem: Cardinality of power set of finite set
•
Combinatorial proof: Cardinality of power set of finite set
▸
Cartesian product
•
What is the Cartesian product?
•
Proving properties of Cartesian product
▸
Converting between set-builder and set-roster notation
•
Converting set-builder notation to set-roster notation
•
Converting set-roster notation to set-builder notation
▸
Converting between set expressions and Venn diagrams
•
Converting a Venn diagram to a set expression
▸
Converting a set expression to a Venn diagram
•
Shading Venn diagrams with two sets
•
Shading Venn diagrams with three sets
•
Set builder notation
•
Converting set theory expressions to predicate logic expressions
•
Disjoint sets
•
Evaluating finite sets using Venn diagrams
•
Georg Cantor
▸
Image and preimage of a set under a function
•
Lesson: What is the image of a set under a function?
•
Proofs: Image and preimage of a set under a function
•
Lesson: What is the preimage of a set under a function?
•
Intersection is largest subset
•
Intro to naive set theory
•
Operations with set-builder notation
•
Power set
•
Proof: Cantor's theorem
•
Proof: Cantor set is uncountable
•
Proof: Cardinality of Cartesian product
•
Proof: Intersection distributes over union
•
Properties of the power set
•
Proving properties of the empty set
•
Proving properties of the subset relation
•
Proving the absorption laws for sets
•
Set-builder notation
•
Set complement
•
Set intersection
•
Set is subset of intersection of supersets
•
Set union
•
Subsets
•
Supersets
•
Union and intersection of a family of sets
•
Union is smallest superset
•
What is symmetric difference?
•
What is the cardinality of a set?
•
Cardinality
›
Naive set theory
Cardinality from Venn diagrams
YouTube videos
829
Set Notation (1 of 3: Intersection, union, size)
Eddie Woo
71654
Use a Venn diagram to Determine Cardinality of Sets (Level 1)
Mathispower4u
71655
Use a Venn diagram to Determine Cardinality of Sets (Level 2)
Mathispower4u