Could one please explain the concept of e-balls in terms of sets. 1. How would one draw an e-ball to indicate that a set is open/closed/neither. How does this transfer to the set complements. 2. How do the intersection of sets work? How does one tell if the intersection of a set is open or closed? Example: Which of the following sets are open, and which are closed? Explain your answers by sketching the sets and open ε-balls. (a) Thecomplement of S={(x;y):x2+y2 ≤5}. (b) The interior of S intersected with T = {(x; y) : x2 + y2 − 4 < 0}
Could one please explain the concept of e-balls in terms of sets. 1. How would one draw an e-ball to indicate that a set is open/closed/neither. How does this transfer to the set complements. 2. How do the intersection of sets work? How does one tell if the intersection of a set is open or closed? Example: Which of the following sets are open, and which are closed? Explain your answers by sketching the sets and open ε-balls. (a) Thecomplement of S={(x;y):x2+y2 ≤5}. (b) The interior of S intersected with T = {(x; y) : x2 + y2 − 4 < 0}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Could one please explain the concept of e-balls in terms of sets.
1. How would one draw an e-ball to indicate that a set is open/closed/neither. How does this transfer to the set complements.
2. How do the intersection of sets work? How does one tell if the intersection of a set is open or closed?
Example:
Which of the following sets are open, and which are closed? Explain your answers by sketching the sets and open ε-balls.
(a) Thecomplement of S={(x;y):x2+y2 ≤5}.
(b) The interior of S intersected with T = {(x; y) : x2 + y2 − 4 < 0}
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