I have the following questions, I understand indexed collections but this one just puzzles me and I dont know where to start, so please if able explain in detail, thank you in advance, Consider the indexed collection {An}neN of sets given byfor every natural number n.d.An = {x € Z : |x| < 42 +n and x < 42/n}e.Show that Unen An = {x € Z : x ≤ 41}.Prove that the sets An are pairwise distinct, i.e. if m, n are natural numberswith m‡n, then Am ‡ An.

d. To show that ⋃n∈NAn={x∈Z:x≤41}, need to prove two inclusions:1. ⋃n∈NAn⊆{x∈Z:x≤41}:Let x be an…

Consider the indexed collection {An}neN of sets given by for every natural number n. d. An = {x € Z |x| < 42 +n and x < 42/n} : e. Show that Unen An = {x € Z :x≤ 41}. Prove that the sets An are pairwise distinct, i.e. if m, n are natural numbers with mn, then Am ‡ An.

Consider the indexed collection {An}neN of sets given by for every natural number n. d. An = {x € Z |x| < 42 +n and x < 42/n} : e. Show that Unen An = {x € Z :x≤ 41}. Prove that the sets An are pairwise distinct, i.e. if m, n are natural numbers with mn, then Am ‡ An.

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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