10:44

Comment on Class Activity 1

08:22

Section 2.5, part 11 Modular arithmetic

09:25

Section 4.5, part 2 Example involving images

07:40

Section 4.5, part 4 Inverse image of unions and of intersections

06:56

Section 4.5, part 5 Image of unions and of intersections

06:08

Section 4.5, part 3 Example involving inverse image

06:07

Section 4.5, part 1 Image and inverse image of sets

06:09

Section 4.3, part 7 Bijections

05:24

Section 4.3, part 6 Example involving injectivity

11:03

Section 4.3, part 8 Bijections and inverses

06:44

Section 4.3, part 5 Injections

08:10

Section 4.3, part 4 Yet another example involving surjectivity

06:04

Section 4.3, part 2 Example involving surjectivity

06:02

Section 4.3, part 3 Another example involving surjectivity

06:42

Section 4.3, part 1 Surjections

06:49

Section 4.2, part 3 Inverse function and composition

10:25

Section 4.2, part 4 Restriction and extension

11:37

Section 4.2, part 2 Composition of functions

03:57

Section 4.2, part 1 Inverse of a function

09:38

Section 4.1, part 2 Some special functions

08:34

Section 4.1, part 1 Functions Basic definitions

13:36

Section 3.3, part 4 Use of equivalence Class Theorem to construct Z from N

14:54

Section 3.4, part 2 Sup and inf

12:22

Section 3.4, part 4 Existence of the square root of 2

14:16

Section 3.4, part 1 Partial orders and linear orders

02:18

Section 3.4, part 3 Completeness property of R

09:26

Section 3.3, part 3 Use of the Equivalence Class Theorem

07:21

Section 3.3, part 2 The Equivalence Class Theorem

08:37

Section 3.3, part 1 Partitions

12:21

Section 3.2, part 5 Equivalence classes of modular arithmetic

08:00

Section 3.2, part 4 Example of equivalence classes

05:57

Section 3.2, part 3 Equivalence classes

06:49

Section 3.2, part 2 Example of equivalence relation

07:42

Section 3.2, part 1 Definition of equivalence relation

13:59

Section 3.1, part 4 General theorems involving relations

09:23

Section 3.1, part 3 Composition of relations

06:28

Section 3.1, part 2 Inverse of a relation

07:15

Section 3.1, part 1 Definition of relation

09:30

2.1, part 1 Basic set theory

06:42

Section 5.1(c), part 7 Cardinality of Cartesian product of finite sets

06:16

Section 5.1(c), part 6 Cardinality of the union of two finite sets.

05:13

Section 5.1(c), part 5 Cardinality of the difference of finite sets

07:41

Section 5.1(c), part 4 Cardinality of subsets of finite sets

11:55

Section 5.1(c), part 3 Cardinality of finite disjoint unions of finite sets

11:53

Section 5.1(c), part 2 Cardinality of a finite set

09:47

Section 5.1(c), part 1 Proof of Pigeonhole Principle

11:30

Section 2.5, part 12 Equivalence of the three kinds of induction

09:38

Section 2.5, part 10 Euclid's Lemma

06:31

Section 2.5, part 8 Square root 2 is irrational

10:48

Section 2.5, part 9 Greatest common divisors

10:38

Section 2.5, part 7 Division Algorithm

07:54

Section 2.5, part 5 Third proof using PCI

04:54

Section 2.5, part 6 Proof of existence in the Fundamental Theorem of Arithmetic

07:59

Section 2.5, part 4 Second proof using PCI

05:14

Section 2.5, part 3 First proof using PCI

06:06

Section 2.5, part 2 An incorrect proof using PCI

04:10

Section 2.5, part 1 Two additional inductive properties of N

14:30

Section 5.2-5.5, part 16 Proof of the Comparability Theorem

06:22

Section 5.2-5.5, part 15 Axiom of Choice and Zorn's Lemma

12:33

Section 5 2-5.5, part 14 Algebraic and transcendental numbers