Proof Index
TOC
Courses
Subreddit
Blog
Search
Search subtopics
Search all
▾
Bridge course
•
Countable and uncountable sets
▸
Proof techniques
•
Example of a nonconstructive proof
•
Direct proof
•
Disproof by counterexample
•
Proof by cases
•
Proving properties of absolute value
•
Proof by contrapositive
•
Proof by contradiction
•
Challenge
•
Proof by induction
•
Proof by strong induction
•
Proving de Moivre's theorem
•
Visual proof
•
Challenge
▸
Relations
•
Equivalence relations
•
Intersection of equivalence relations
•
Representing relations using matrices
▸
Combining relations
•
Composition of relations
•
Inverse of composite relation
•
Representing relations using digraphs
•
Properties of relations
•
Proving equivalence relations
•
What is a relation?
•
Finding the inverse of a relation on a finite set
▸
Functions (bridge course)
▸
Injective, surjective, and bijective
•
Intro
•
Is it bijective? (infinite domain)
•
Is it injective?
▸
Is it surjective?
•
Proof: Composite of surjections is surjection
•
Proving properties of injective, surjective, and bijective functions
›
Bridge course
Functions (bridge course)
Injective, surjective, and bijective
Other resources