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Problem 16. Let K be the set of all functions from IN to the set {I, Love, You}. K={ff: N- {I, Love, You} is a function} For example, the following functions are elements of K if n is odd Love if n is even." f(n) = {! It might help to view the above functions as follows: Prove that K is an uncountable set. g(n)= Love You 1 2 3 4 5 L I L I YILY fI 8 L ... ... if n = 3k, kEN if n = 3k +1,k € N if n = 3k+2, kEN.

Problem 16. Let K be the set of all functions from IN to the set {I, Love, You}. K={ff: N- {I, Love, You} is a function} For example, the following functions are elements of K if n is odd Love if n is even." f(n) = {! It might help to view the above functions as follows: Prove that K is an uncountable set. g(n)= Love You 1 2 3 4 5 L I L I YILY fI 8 L ... ... if n = 3k, kEN if n = 3k +1,k € N if n = 3k+2, kEN.

Advanced Engineering Mathematics
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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Problem 16. Let X be the set of all functions from IN to the set {I, Love, You}. K={ff: N- {I, Love, You} is a function} For example, the following functions are elements of K f(n)= Love if n is odd if n is even. It might help to view the above functions as follows: 8 Prove that K is an uncountable set. 1 g(n)= Love You 2 3 4 5 LIL I ILY LY if n=3k, k EIN if n = 3k+1, k EN if n = 3k+2, kEN.
Transcribed Image Text:Problem 16. Let X be the set of all functions from IN to the set {I, Love, You}. K={ff: N- {I, Love, You} is a function} For example, the following functions are elements of K f(n)= Love if n is odd if n is even. It might help to view the above functions as follows: 8 Prove that K is an uncountable set. 1 g(n)= Love You 2 3 4 5 LIL I ILY LY if n=3k, k EIN if n = 3k+1, k EN if n = 3k+2, kEN.
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