5)a) It is known that Q ͠ N (Rational Numbers have the same power as the Natural Numbers set N.). So show that QxQ ͠ N. ( QxQ have the same power as the N )
5)a) It is known that Q ͠ N (Rational Numbers have the same power as the Natural Numbers set N.). So show that QxQ ͠ N. ( QxQ have the same power as the N )
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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5)a) It is known that Q ͠ N (Rational Numbers have the same power as the Natural Numbers set N.). So show that QxQ ͠ N. ( QxQ have the same power as the N )
b)The set of all closed intervals whose endpoints are rational numbers( that is, show that set { [a,b] , a ɛ Q , b ɛ Q , a<b } is the same power as the natural number set N.
(Definition: Let A and B be two sets.If there is a one-to-one function from A to B and at least one overlying function, it is said that A set has the same power as set B. and shown to be A ͠ B)
(It's abstract mathematics, please can you write step-by-step solutions I have a shortcoming in this regard.)
![5) a) Q- N olduêu bilinmekte dir, Bunca
göre
Qx Q~ N olduğure gösteriniz.
b) Ua noktaları rosyonel sayılar olon budün
tapalı aralikların oluşdurduğu
{ [aib]:Q€Q, bE Q acbj kimesinin doğale
kimenin, yani
sayılar kimes, N
N ile oypı kuvvedde oldiğunu gösteiniz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0b363a3-a225-4708-917e-472c6a158b01%2F13de5e1e-004a-41d7-94f2-3f3780f7e78a%2Fstfbm1q_processed.png&w=3840&q=75)
Transcribed Image Text:5) a) Q- N olduêu bilinmekte dir, Bunca
göre
Qx Q~ N olduğure gösteriniz.
b) Ua noktaları rosyonel sayılar olon budün
tapalı aralikların oluşdurduğu
{ [aib]:Q€Q, bE Q acbj kimesinin doğale
kimenin, yani
sayılar kimes, N
N ile oypı kuvvedde oldiğunu gösteiniz
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