Real Analysis






Real Analysis Course


Section 1.2 Mathematical Induction
Section 2.1 The Algebraic and Ordering Property of the Reals
Section 2.2 Absolute value and the real line
Section 2.3 The Completeness property of R
Section 2.4 Applications of the supremum property
Section 3.1 Sequences and limits
Section 3.2 Limit theorems
Section 3.3 Monotone sequences
Section 3.4 Subsequences and the Bolzano-Weierstrass Theorem
Section 3.5 Cauchy Criteria
Section 3.6 Properly Divergent Sequences
Section 4.1 Limits of functions
Section 4.2 Limits Theorems
Section 5.1 Continuous functions
Section 5.2 Combination of continuous functions
Section 5.3 Continuous functions on intervals
Section 5.4 Uniform continuity

At 8:40, the result in the bracket should be [(2l)^3+3(2l)^2+3(2l)+1].
However, it doesn’t affect the answer at all (Correction by Zenan)


At 2:29, I should have used the real number -2 as my lower bound. Clearly, 0 cannot be a lower bound for A. So please, replace 0 with another lower bound such as -2. Thanks to Arthur Farias for the correction



At 38:43, I should also add the following. We select (or fix) such a natural number N.

Correction by Arthur Farias
@ 22:18, the function is unbounded. Not bounded. Thanks to Arthur for the correction.