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Exercise 3. Let Inf(N) be the set of infinite subsets of N. Prove that Inf (N) P(N). Exercise 4. Let D(N) be the set of weakly decreasing functions f : N → N; ie. those functions ƒ such that f(n) ≥ f(m) for all 0 ≤ n < m. Prove that D(N) ≈ N.

Exercise 3. Let Inf(N) be the set of infinite subsets of N. Prove that Inf (N) P(N). Exercise 4. Let D(N) be the set of weakly decreasing functions f : N → N; ie. those functions ƒ such that f(n) ≥ f(m) for all 0 ≤ n < m. Prove that D(N) ≈ N.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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Exercise 3. Let Inf(N) be the set of infinite subsets of N. Prove that Inf (N) P(N). Exercise 4. Let D(N) be the set of weakly decreasing functions f : N → N; ie. those functions ƒ such that f(n) ≥ f(m) for all 0 ≤ n < m. Prove that D(N) ≈ N.
Transcribed Image Text:Exercise 3. Let Inf(N) be the set of infinite subsets of N. Prove that Inf (N) P(N). Exercise 4. Let D(N) be the set of weakly decreasing functions f : N → N; ie. those functions ƒ such that f(n) ≥ f(m) for all 0 ≤ n < m. Prove that D(N) ≈ N.
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