37. For a set A, let P(A) be the set of all subsets of A. Prove that A is not equivalent to P(A). (Hint: Suppose f: A→ P(A) and define C = (x:x EA and x # f(x)}, Show Cim fil
37. For a set A, let P(A) be the set of all subsets of A. Prove that A is not equivalent to P(A). (Hint: Suppose f: A→ P(A) and define C = (x:x EA and x # f(x)}, Show Cim fil
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![set of algebraic numbers is a countable set.
37. For a set A, let P(A) be the set of all subsets of A. Prove that A is not equivalent to P(A).
(Hint: Suppose f: A → P(A) and define C =
38. Let a, b, c, and d be any real numbers such that a < b and c < d. Prove that [a, b] is
{(x:x EA and x # f(x)}. Show C# im f.)
equivalent to [c, d]. (Hint: Show that [a, b] is equivalent to [0, 1] first.)
0.5 REAL NUMBERS](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd597ffd2-5c4b-4c2e-8332-77ce1607dac1%2F3c5f0c87-9d5b-420b-b240-64247ea0e5af%2Fcua5uzq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:set of algebraic numbers is a countable set.
37. For a set A, let P(A) be the set of all subsets of A. Prove that A is not equivalent to P(A).
(Hint: Suppose f: A → P(A) and define C =
38. Let a, b, c, and d be any real numbers such that a < b and c < d. Prove that [a, b] is
{(x:x EA and x # f(x)}. Show C# im f.)
equivalent to [c, d]. (Hint: Show that [a, b] is equivalent to [0, 1] first.)
0.5 REAL NUMBERS
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