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Suppose we know that each of An, n ≥ 0, is countable. Show that (a) {A0, A₁,..., An...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! (b)(KS) Prove that U> A; is countable. (c) S) Did Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words.

Suppose we know that each of An, n ≥ 0, is countable. Show that (a) {A0, A₁,..., An...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! (b)(KS) Prove that U> A; is countable. (c) S) Did Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words.

Advanced Engineering Mathematics
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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7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a)) {A0, A₁, A,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! ES) Prove that U20 A; is countable. (c) Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words.
Transcribed Image Text:7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a)) {A0, A₁, A,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! ES) Prove that U20 A; is countable. (c) Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words.
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