The question is the last two sentences in the picture. Above it is information to help solve the question Note. If B is a subset of A and A is countable then B is countable. To see this leta1, a2 . . . be a sequence whose range is A. This means that every agis a member of Aand every member of A is ar for some k . Then define the sequence b1, b2, ... in thefollowing way. Let ji be the first integer j such that a, e B. Given that jr has beenfound, let jk+1 be the first integer j > jk such that a; e B. Do this for k = 1, 2, ....Let br%3Dajrfor k = 1, 2,.... The sequence b1, b2 . .. will have range B.%3!Note. According to the definition, when each of A and B is a set, |B| < |A| meansthat there is a one-to-one function from B into A.Suppose that B is a subset of A. Specify a one-to-one function whose domain is B andwhose range is a subset of A.By doing this you will show that |B| < |A|

suppose that B is a subset of A claim- to find a one-to-one function whose domain is B and range is…

Answered: Suppose that B is a subset of A.…

Suppose that B is a subset of A. Specify a one-to-one function whose domain is B and whose range is a subset of A.By doing this you will show that |B| < |A||

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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The question is the last two sentences in the picture. Above it is information to help solve the question

Note. If B is a subset of A and A is countable then B is countable. To see this let
a1, a2 . . . be a sequence whose range is A. This means that every agis a member of A
and every member of A is ar for some k . Then define the sequence b1, b2, ... in the
following way. Let ji be the first integer j such that a, e B. Given that jr has been
found, let jk+1 be the first integer j > jk such that a; e B. Do this for k = 1, 2, ....
Let br
%3D
ajr
for k = 1, 2,.... The sequence b1, b2 . .. will have range B.
%3!
Note. According to the definition, when each of A and B is a set, |B| < |A| means
that there is a one-to-one function from B into A.
Suppose that B is a subset of A. Specify a one-to-one function whose domain is B and
whose range is a subset of A.By doing this you will show that |B| < |A|

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