Monotone Sequences - Real Analysis | Lecture 4

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In this lecture we discuss increasing and decreasing sequences. Such sequences are referred to as monotone, and we prove that when they are bounded they must converge. We use these results to then introduce the limit superior and limit inferior, which are generalizations of the limit of a sequence. Importantly, limit superior and inferior always exist, even when the sequence does not converge, and furthermore, they coincide with the limit of a convergent sequence. We provide illustrative worked examples to illuminate the key concepts of the lecture.

This course is taught by Jason Bramburger
  1. Jason Bramburger
  2. monotone
  3. sequence
  4. increasing
  5. decreasing
  6. limit superior
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Комментарии
Автор

I was just learning this! It is nice to have a new lecture to go along with my notes. Thanks for the video!

LucasDimoveo
Автор

Hi Jason. Firstly, thank you so much for the excellent lectures. Are there any notes that I can use along with these videos? (I am self-learning real analysis).

midhununni