402.3A2 Isolated Points and Discrete Sets

Описание к видео 402.3A2 Isolated Points and Discrete Sets

Where interior points of a set A have an ε-neighborhood that is ENTIRELY comprised of points of A, isolated points have an ε-neighborhood that contains NO points of A, apart from themselves. Sets whose points are all isolated are called discrete sets. See the playlist: http://matthematics.com/real

0:00 Introduction
1:14 Motivation for Isolated Points vs. Interior Points
3:22 Definition of Isolated Point
5:22 Definition of Discrete Set
5:37 Example: The Integers are Discrete in R
7:40 Example: Is This a Discrete Set?
10:19 Limits of Sequences are (Usually) Not Isolated

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