Real Analysis I (V-U)

• Informal Introduction to the course (V-U)
• Informal Introduction (V-U)
• Basic Set Theory (V-U)
• Some Properties Of Positive Integers (V-U)
• Set Of Integers (V-U)
• Finite and Infinite Sets: initial segments & Cardinality (V-U)
• Finite and Infinite Sets: Dedekind Infinite Set (V-U)
• The Field (V-U)
• The Set Of Rational Numbers (V-U)
• The Gaps In the Rational Numbers: p^2 =2 solution (V-U)
• Ordered Set (V-U)
• Lower and Upper Bounds (V-U)
• Supremum And Infimum Examples (V-U)
• The Least Upper Bound Property (V-U)
• The Completeness Axiom (V-U)
• The Achimedean Property (V-U)
• The Set Of Rationals Is Dense In R (V-U)
• The Set Of Rationals Is Not Complete (V-U)
• The Set Of Irrationals Is Dense In R (V-U)
• Field Properties Some Conclusions (V-U)
• The Triangular Inequality (V-U)
• Theorem (V-U)
• The Extended Real Number System (V-U)
• The Principle Of Mathematical Induction (V-U)
• The Principle Of Mathematical Induction: Examples (V-U)