real numbers

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1. 1▶Lecture 11: Extreme and Intermediate Value Theorem; Metric SpacesMIT 18.100B Real Analysis, Spring 2025Notes
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2. 2▶Lecture 8: Convergence Tests for Series; Power SeriesMIT 18.100B Real Analysis, Spring 2025Notes
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3. 3▶Lecture 9: Limsup and Liminf; Power Series; Continuous Functions; Exponential FunctionMIT 18.100B Real Analysis, Spring 2025Notes
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4. 4▶Lecture 4: Sequences; ConvergenceMIT 18.100B Real Analysis, Spring 2025Notes
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5. 5▶Lecture 3: How to Write a Proof; Archimedean PropertyMIT 18.100B Real Analysis, Spring 2025Notes
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6. 6▶Lecture 1: Introduction to Real NumbersMIT 18.100B Real Analysis, Spring 2025Notes
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7. 7▶Lecture 10: Continuous Functions; Exponential Function (cont.)MIT 18.100B Real Analysis, Spring 2025Notes
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8. 8▶Lecture 5: Monotone Convergence TheoremMIT 18.100B Real Analysis, Spring 2025Notes
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9. 9▶Lecture 6: Cauchy Convergence TheoremMIT 18.100B Real Analysis, Spring 2025Notes
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10. 10▶Review for 18.100B Real Analysis MidtermMIT 18.100B Real Analysis, Spring 2025Notes
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11. 11▶Lecture 13: Limits of FunctionsMIT 18.100A Real Analysis, Fall 2020Notes
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12. 12▶Lecture 8: The Squeeze Theorem and Operations Involving Convergent SequencesMIT 18.100A Real Analysis, Fall 2020Notes
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13. 13▶Lecture 11: Absolute Convergence and the Comparison Test for SeriesMIT 18.100A Real Analysis, Fall 2020Notes
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14. 14▶Lecture 6: The Uncountabality of the Real NumbersMIT 18.100A Real Analysis, Fall 2020Notes
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15. 15▶Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's FunctionMIT 18.100A Real Analysis, Fall 2020Notes
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16. 16▶Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite SeriesMIT 18.100A Real Analysis, Fall 2020Notes
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17. 17▶Lecture 12: The Ratio, Root, and Alternating Series TestsMIT 18.100A Real Analysis, Fall 2020Notes
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18. 18▶Lecture 14: Limits of Functions in Terms of Sequences and ContinuityMIT 18.100A Real Analysis, Fall 2020Notes
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19. 19▶Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute ValueMIT 18.100A Real Analysis, Fall 2020Notes
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20. 20▶Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound PropertyMIT 18.100A Real Analysis, Fall 2020Notes
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