For each positive integer n, consider the closed interval [ Similarly, consider the open intervals (a) If N is a positive integer, express the set as an interval. (b) Let us define Cn := as an interval. (d) Define the set Dn:=(-n,n). C₂C₂C₂n...n CN How many different elements belong to C? Sidenote: This is how we can define intersection for infinitely many sets. (c) If N is a positive integer, express the set D₁ UD₂U...UDN C:= {r € R: for each positive integer n, z € C₂}. D:= {TER:r € D₁, for some n € N}. Describe in an alternative way the set R \ D. Sidenote: This is how we can define the union of infinitely many sets.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I've understood abc but d.

For a, Cn = close interval -1/N ,1/N

For b, C =0

For c, Dn = open interval -N, N

What is the correct steps for part d? By letting D goes to infinity?

 

For each positive integer n, consider the closed interval
[
Similarly, consider the open intervals
(a) If N is a positive integer, express the set
as an interval.
(b) Let us define
Cn :=
as an interval.
(d) Define the set
Dn:=(-n,n).
C₂C₂C₂n...n CN
How many different elements belong to C?
Sidenote: This is how we can define intersection for infinitely many sets.
(c) If N is a positive integer, express the set
D₁ UD₂U...UDN
C:= {r € R: for each positive integer n, z € C₂}.
D:= {TER:r € D₁, for some n € N}.
Describe in an alternative way the set R \ D.
Sidenote: This is how we can define the union of infinitely many sets.
Transcribed Image Text:For each positive integer n, consider the closed interval [ Similarly, consider the open intervals (a) If N is a positive integer, express the set as an interval. (b) Let us define Cn := as an interval. (d) Define the set Dn:=(-n,n). C₂C₂C₂n...n CN How many different elements belong to C? Sidenote: This is how we can define intersection for infinitely many sets. (c) If N is a positive integer, express the set D₁ UD₂U...UDN C:= {r € R: for each positive integer n, z € C₂}. D:= {TER:r € D₁, for some n € N}. Describe in an alternative way the set R \ D. Sidenote: This is how we can define the union of infinitely many sets.
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