1-Let B be the set of all infinite sequences over {0, 1}. Is this set countable or not, prove it?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.5: Mathematical Induction
Problem 33E
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1-Let B be the set of all infinite sequences over {0, 1}. Is this set countable or not, prove it?
2- consider the set of all finite subsets of N, is this set countable or not, prove it?
3- if a belongs to the set of all even natural numbers, and b belongs to the set of natural numbers divisible
by 3. Is the set of fractions a/b countable or uncountable, prove it?
Transcribed Image Text:1-Let B be the set of all infinite sequences over {0, 1}. Is this set countable or not, prove it? 2- consider the set of all finite subsets of N, is this set countable or not, prove it? 3- if a belongs to the set of all even natural numbers, and b belongs to the set of natural numbers divisible by 3. Is the set of fractions a/b countable or uncountable, prove it?
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