Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem

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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez

We prove some of the most useful tools of calculus: the Min/Max theorem or the Extreme Value Theorem (EVT) and the Intermediate Value Theorem (IVT). Is every hypothesis in these theorems required?

License: Creative Commons BY-NC-SA

  1. MIT OpenCourseWare
  2. EVT
  3. Extreme Value Theorem
  4. IVT
  5. Intermediate Value Theorem
  6. Min/Max Theorem
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Комментарии
Автор

Hey self-learners! Be aware of a minor typo at 55:18. It should be b_(n-1) not b_(n-2). FANTASTIC LECTURE MIT ocw!

nicolasg.b.
Автор

41:55 love how it "pains [him]" to say the definition of continuity is the fact that you can draw a function without picking up the chalk since that's what we all learned in high school. Frankly I like the real analysis definition a lot more too, but I can't really think of any counterexamples of the "don't pick up your chalk" example, aside from the fact that it isn't exactly rigorous. Great way to introduce the concept to those not as interested in math.

nathanielthomas
Автор

To do the negation he used a direct proof with contradiction

Jay-tzb