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denumerable. Apply the definition and prove that the set A = {₁, {} ... } is

denumerable. Apply the definition and prove that the set A = {₁, {} ... } is

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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Prove that the set of natural numbers is infinite. ·Let : NÈ F(n) = 2n F is Bijection? Yes • One-to-one ?yelet F(x) = f(y) for some X, YE N then 2x=2y => x=y + onto Et? YLet weE, JKEN Such that W=2k. Need tEN Such that 200 Flts=w EN zt=w => t = @=22=k Choose t-k F(t)=2t=2(2)=w •Conclusion: F is Criterion implies that because ECN and E and N are equivalent, N has to be infinite. The End. =>> • E= { Even Positive Integers} = ³n; n=2k For KENY 5 CN Proper subset or t = w 2 a bijection. EN
Transcribed Image Text:Prove that the set of natural numbers is infinite. ·Let : NÈ F(n) = 2n F is Bijection? Yes • One-to-one ?yelet F(x) = f(y) for some X, YE N then 2x=2y => x=y + onto Et? YLet weE, JKEN Such that W=2k. Need tEN Such that 200 Flts=w EN zt=w => t = @=22=k Choose t-k F(t)=2t=2(2)=w •Conclusion: F is Criterion implies that because ECN and E and N are equivalent, N has to be infinite. The End. =>> • E= { Even Positive Integers} = ³n; n=2k For KENY 5 CN Proper subset or t = w 2 a bijection. EN
denumerabie. Apply the definition and prove that the set A = { ¹, .} is ...
Transcribed Image Text:denumerabie. Apply the definition and prove that the set A = { ¹, .} is ...
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