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Pigeonhole via functions.
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Classroom Contents
Proof Writing - Introduction to Mathematical Proofs and Set Theory
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- 1 Introduction to Sets
- 2 The Basics of Sets | Cartesian Products
- 3 Basic Set Operations
- 4 Indexed Sets
- 5 Mathematical Statements
- 6 Logic Operations.
- 7 Conditional Statements
- 8 Quantifiers.
- 9 Counting
- 10 Inclusion-Exclusion.
- 11 Hierarchy of Results/Direct Proof
- 12 Proofs involving cases.
- 13 The contrapositive.
- 14 Proofs by contradiction.
- 15 a cornucopia of proofs!
- 16 Basic proofs involving sets.
- 17 A few more proofs involving sets.
- 18 Proving statements false.
- 19 Proofs by mathematical induction.
- 20 Strong induction.
- 21 more induction!
- 22 Relations on a set.
- 23 Equivalence Relations
- 24 Equivalence Relations and Partitions
- 25 Some important facts about ≡ (mod n)
- 26 What really is a function?
- 27 Pigeonhole via functions.
- 28 Composition of functions -- injectivity and surjectivity.
- 29 Inverse Functions
