Superquiz 1 Solutions

Need a video that goes over the solutions to an exam that covers the basics of a real analysis class? I got you covered.

0:00, Problem 1 Set Theory (Union, Intersection, Proper Subset)
3:20, Problem 2 Set Theory (Empty, Subset)
5:08, Problem 3 Injective and Surjective Functions
13:53, Problem 4 Codomain vs. Range
16:33, Problem 5 Triangle Inequality (and Reverse Triangle Inequality)
17:46, Problem 6 Absolute Values and Inequalities
20:45, Problem 7 Definition of Supremum and Infimum
23:54, Problem 8 Computing the Supermum and Infimum
26:20, Problem 9 Axiom of Completeness
27:24, Problem 10 Nested Interval Property
28:52, Problem 11 Cardinality: Finite vs. Countably Infinite vs. Uncountably Infinite
32:21, Problem 12 Cantor's Diagonalization Argument for ℚ
37:54, Problem 13 Definition of Sequence Convergence
40:21, Problem 14 Using Sequential Limit Properties
46:24, Problem 15 Monotone Convergence Theorem and Bolzano–Weierstrass Theorem
49:18, Problem 16 Definition of Cauchy Sequence
50:38, Problem 17 Series
54:13, Problem 18 An Open Set that is not an Interval
1:04:56, Problem 19 Open or Closed?
1:08:33, Problem 20 Compact Subsets
1:11:07, Problem 21 Functional Limit Definition
1:15:27, Problem 22 Clever Carl: Algebraic Limit Properties
1:18:58, Problem 23 Characterizations of Continuity
1:23:14, Problem 24 Example of Continuity except at boundary points
1:26:00, Problem 25 Algebraic Continuity Theorem
1:27:47, Problem 26 Continuous Functions on Compact Sets
1:30:35, Problem 27 Intermediate Value Theorem (Applied)
1:33:30, Problem 28 Characterizations of the Derivative
1:37:26, Problem 29 Product Rule for Derivatives?
1:40:33, Problem 30 Interior Extremum Theorem and Darboux's Theorem
1:43:59, Problem 31 Mean Value Theorem and Rolle's Theorem
1:47:41, Problem 32 Lower and Upper Sums and Integrals; Integrability
1:56:34, Problem 33 Basic Properties of the Darboux Integral
2:01:08, Problem 34 First Fundamental Theorem of Calculus
2:03:06, Problem 35 Statement of the Second Fundamental Theorm of Calculus
2:05:06, Problem 36 FTOC-2 vs. Integration