Consider the indexed collection {An}neN of sets given by for every natural number n. a. b. An = {x € Z : |x| < 42 +n and x < 42/n} C. Evaluating the definitions, we have A₁ scribe the sets A2, A3, and A42; Show that 0 EnEN An. = {-42, -41,...,4 1,...,41}. Similarly de- Determine the intersection EN An.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I have the following question, please if able explain them in detail, I understand the general idea of indexed collections, but this one's just a bit too complex for me,

Consider the indexed collection {AnneN of sets given by
for every natural number n.
a.
b.
An = {x € Z : |x| < 42 +n and x < 42/n}
C.
Evaluating the definitions, we have A₁
scribe the sets A2, A3, and A42;
Show that 0 EnEN An.
-
{-42, -41,..., 41}. Similarly de-
Determine the intersection ne An.
Transcribed Image Text:Consider the indexed collection {AnneN of sets given by for every natural number n. a. b. An = {x € Z : |x| < 42 +n and x < 42/n} C. Evaluating the definitions, we have A₁ scribe the sets A2, A3, and A42; Show that 0 EnEN An. - {-42, -41,..., 41}. Similarly de- Determine the intersection ne An.
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